Fair Value Measurements - Additional information (Detail)	Jun. 30, 2015 USD ($)
Fair Value Disclosures [Abstract]
Transfer of investments between Levels 1 and 2	$ 0

Fair Value Assets And Liabilities Transfers Between Level One And Level Two Amount

No definition available.

Name:	dgica_FairValueAssetsAndLiabilitiesTransfersBetweenLevelOneAndLevelTwoAmount
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant