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Borrowings - Amount of FHLB of Indianapolis/Pittsburgh Stock Purchased, Collateral Pledged and Assets Related to MICO's/Atlantic States Agreement (Parenthetical) (Detail) | Dec. 31, 2019 USD ($)
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FHLB of Pittsburgh [Member] | Atlantic States [Member] |
Line of Credit Facility [Line Items] |
Collateral Pledged at carrying value | $ 36,295,910

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- Definition Pledged assets separately reported assets pledged as collateral at carrying value. + References No definition available. + Details
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Namespace Prefix: | dgica_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | dei_LegalEntityAxis=dgica_AtlanticStatesMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |