Extensions 1→N→G→Q→1 with N=Dic₇ and Q=S₃

Direct product G=NxQ with N=Dic₇ and Q=S₃

		d	ρ	Label	ID
S₃xDic₇		84	4-	S3xDic7	168,13

Semidirect products G=N:Q with N=Dic₇ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₇:S₃ = C₇:D₁₂	φ: S₃/C₃ → C₂ ⊆ Out Dic₇	84	4+	Dic7:S3	168,17
Dic₇:₂S₃ = D₂₁:C₄	φ: trivial image	84	4+	Dic7:2S3	168,14

Non-split extensions G=N.Q with N=Dic₇ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₇.S₃ = C₂₁:Q₈	φ: S₃/C₃ → C₂ ⊆ Out Dic₇	168	4-	Dic7.S3	168,18

Extensions 1→N→G→Q→1 with N=Dic7 and Q=S3