Name:	dgica_MinimumPercentageOfExcessClassACommonStockDividendOverClassBDividend
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Data Type:	dtr:percentItemType
Balance Type:	na
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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.

No definition available.

Name:	us-gaap_EquityClassOfTreasuryStockLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

Number of shares remaining authorized to be purchased under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership.

No definition available.

Name:	us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

Number of shares that have been repurchased during the period and have not been retired and are not held in treasury. Some state laws may govern the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock.

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Name:	us-gaap_StockRepurchasedDuringPeriodShares
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Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

Number of previously issued common shares repurchased by the issuing entity and held in treasury.

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Name:	us-gaap_TreasuryStockCommonShares
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
Namespace Prefix:
Data Type:	na
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Period Type: