Earnings Per Share - Additional Information (Detail)	9 Months Ended
Sep. 30, 2017
Equity [Abstract]
Minimum percentage of class A common stock declared dividend excess over class B dividend	10.00%

Minimum percentage of excess class A common stock dividend over class B dividend.

No definition available.

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