Earnings Per Share - Additional Information (Detail)	3 Months Ended
Mar. 31, 2014
Equity [Abstract]
Percentage of dividend declared on each share	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