Net Income Per Share (Details)	6 Months Ended
Jun. 30, 2025
Net Income Per Share [Abstract]
Minimum percentage of class A common stock declared dividend excess over class B dividend	10.00%

The minimum percentage of excess class A common stock dividend over class B dividend for declaration and payment of cash dividends.

No definition available.

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