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Earnings Per Share - Additional Information (Detail) | 6 Months Ended
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Jun. 30, 2021
Earnings Per Share [Abstract] |
Minimum percentage of class A common stock declared dividend excess over class B dividend | 10.00%

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- Definition Minimum percentage of excess class A common stock dividend over class B dividend. + References No definition available. + Details
Name: | dgica_MinimumPercentageOfExcessClassACommonStockDividendOverClassBDividend
Namespace Prefix: | dgica_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | duration

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- References No definition available. + Details
Name: | us-gaap_EarningsPerShareAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration