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Income Taxes - Additional Information (Detail) (USD $)
3 Months Ended
Mar. 31, 2015
Dec. 31, 2014
Operating Loss Carryforwards [Line Items]    
Deferred tax asset, net 42,100,000dgica_DeferredTaxAssets $ 41,700,000dgica_DeferredTaxAssets
Alternative minimum tax credit carryforward 11,000,000dgica_DeferredTaxAssetsTaxCreditCarryforwardsAlternativeMinimumTaxAmount  
Earliest Tax Year [Member]    
Operating Loss Carryforwards [Line Items]    
Tax years open for examination 2011  
Latest Tax Year [Member]    
Operating Loss Carryforwards [Line Items]    
Tax years open for examination 2014  
Le Mars [Member]    
Operating Loss Carryforwards [Line Items]    
Valuation allowance related to the portion of operating loss carryforwards 440,778us-gaap_OperatingLossCarryforwardsValuationAllowance
/ dei_LegalEntityAxis
= dgica_LeMarsMember
 
Operating loss carryforwards 3,900,000us-gaap_OperatingLossCarryforwards
/ dei_LegalEntityAxis
= dgica_LeMarsMember
 
Operating loss carryforwards expiration period 2020  
Operating loss carryforwards annual limitations in amount on use 376,000dgica_OperatingLossCarryforwardsAnnualLimitationsInAmountOnUse
/ dei_LegalEntityAxis
= dgica_LeMarsMember