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Namespace Prefix:	dgica_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

Minimum time of service required for an employee group to become eligible to participate in the plan.

No definition available.

Name:	dgica_EBPMinimumTimeOfServiceToBeEligibleToParticipateInPlan
Namespace Prefix:	dgica_
Data Type:	xbrli:durationItemType
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Period Type:	duration

Age at which a participant may elect early retirement under the terms of the employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

No definition available.

Name:	dgica_EmployeeBenefitPlanEarlyRetirementAge
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Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

Percentage of company contributions and related earnings that is nonforfeitable to a participant after completion of the specified period of credited service under the terms of the plan employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

No definition available.

Name:	dgica_EmployeeBenefitPlanEmployerContributionVestingPercentage
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Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	instant

The automatic annual percentage increase applied to a plan participant's salary deferral rate under an employee benefit/retirement plan.

No definition available.

Name:	dgica_EmployeeBenefitPlanParticipantContributionAutomaticAnnualDeferralRateIncrease
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Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

Percentage of minimum pretax annual compensation that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)), is permitted to contribute to total pretax annual compensation.

No definition available.

Name:	dgica_EmployeeBenefitPlanParticipantContributionPretaxMinimumAnnualCompensationToTotalCompensationPercentage
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Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

Age at which a participant attains normal retirement under the terms of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

No definition available.

Name:	dgica_EmployeeBenefitPlanParticipantRetirementAge
Namespace Prefix:	dgica_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

Maximum threshold age of participant to roll over vested balance, if no election is made, to an individual retirement account in accordance with the plan provisions under the employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

No definition available.

Name:	dgica_EmployeeBenefitPlanThresholdAutomaticRolloverAge
Namespace Prefix:	dgica_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

Employee benefit plan, threshold vesting percentage required for forfeitures.

No definition available.

Name:	dgica_EmployeeBenefitPlanThresholdVestingPercentageForForfeitures
Namespace Prefix:	dgica_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

Amount of benefit plan, in vested account, no longer allocated to participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

No definition available.

Name:	dgica_EmployeeBenefitPlanVestedAccount
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

The period an employee must work before becoming fully vested, 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

No definition available.

Name:	dgica_EmployeeBenfitPlanEmployerContributionVestingPeriod
Namespace Prefix:	dgica_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

Indicates (true false) whether description of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) is published and made available.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:booleanItemType
Balance Type:	na
Period Type:	duration

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-SubTopic 205
-Topic 962
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

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Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

Percentage of employer matching contribution on eligible participant contribution to employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

Name:	us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Percentage of participant compensation eligible for employer matching contribution for participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

Name:	us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Amount of plan asset, in forfeited nonvested account, no longer allocated to participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

Name:	us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount of decrease in forfeited nonvested account of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) from employer contribution.

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 962
-SubTopic 325
-Name Accounting Standards Codification
-Section 55
-Paragraph 17
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478873/962-325-55-17

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (j)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-04(5)(c))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Percentage of eligible compensation contributed for participant automatically enrolled in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

Name:	us-gaap-ebp_EmployeeBenefitPlanParticipantContributionAutomaticDeferralRate
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Percentage of maximum pretax annual compensation that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)), is permitted to contribute to total pretax annual compensation.

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Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Name:	dei_LegalEntityAxis=dgica_EBP003Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestAxis=dgica_EmployeesRegularlyScheduledMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestAxis=dgica_PartTimeAndTemporaryEmployeesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestAxis=dgica_PartTimeAndTemporaryEmployeesHoursPerTwoYearsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanParticipantDirectedStatusAxis=dgica_ParticipantsGenerallyWillReceiveALumpSumDistributionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanParticipantDirectedStatusAxis=dgica_ParticipantsMayReceiveALumpSumDistributionOrADirectRolloverToAnIndividualRetirementAccountMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanParticipantDirectedStatusAxis=dgica_ParticipantsAssetsWillGenerallyBeHeldInThePlanUntilTheRetirementOrEarlyRetirementAgeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap-ebp_EmployeeBenefitPlanContributionParticipatingEmployerAxis=dgica_ParticipantsInitial3ContributionsEligibleFor100CompanyMatchingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: