v3.10.0.1

Earnings Per Share - Additional Information (Detail) - shares	3 Months Ended		9 Months Ended
	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2018	Sep. 30, 2017
Earnings Per Share [Abstract]
Minimum percentage of class A common stock declared dividend excess over class B dividend			10.00%
Options excluded from diluted earnings per share	6,731,481	5,178,629		1,382,400

X

- Definition

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

+ References

No definition available.

+ Details

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

X

- Definition

Securities (including those issuable pursuant to contingent stock agreements) that could potentially dilute basic earnings per share (EPS) or earnings per unit (EPU) in the future that were not included in the computation of diluted EPS or EPU because to do so would increase EPS or EPU amounts or decrease loss per share or unit amounts for the period presented.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=6371337&loc=d3e3550-109257

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration