Extensions 1→N→G→Q→1 with N=C₇×Q₈ and Q=S₃

Direct product G=N×Q with N=C₇×Q₈ and Q=S₃

		d	ρ	Label	ID
S₃×C₇×Q₈		168	4	S3xC7xQ8	336,190

Semidirect products G=N:Q with N=C₇×Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×Q₈)⋊₁S₃ = Q₈⋊D₂₁	φ: S₃/C₁ → S₃ ⊆ Out C₇×Q₈	56	4+	(C7xQ8):1S3	336,119
(C₇×Q₈)⋊₂S₃ = C₇×GL₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₇×Q₈	56	2	(C7xQ8):2S3	336,116
(C₇×Q₈)⋊₃S₃ = Q₈⋊₂D₂₁	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	168	4+	(C7xQ8):3S3	336,103
(C₇×Q₈)⋊₄S₃ = Q₈×D₂₁	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	168	4-	(C7xQ8):4S3	336,200
(C₇×Q₈)⋊₅S₃ = Q₈⋊₃D₂₁	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	168	4+	(C7xQ8):5S3	336,201
(C₇×Q₈)⋊₆S₃ = C₇×Q₈⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	168	4	(C7xQ8):6S3	336,87
(C₇×Q₈)⋊₇S₃ = C₇×Q₈⋊₃S₃	φ: trivial image	168	4	(C7xQ8):7S3	336,191

Non-split extensions G=N.Q with N=C₇×Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×Q₈).₁S₃ = Q₈.D₂₁	φ: S₃/C₁ → S₃ ⊆ Out C₇×Q₈	112	4-	(C7xQ8).1S3	336,118
(C₇×Q₈).₂S₃ = C₇×CSU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₇×Q₈	112	2	(C7xQ8).2S3	336,115
(C₇×Q₈).₃S₃ = C₂₁⋊₇Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	336	4-	(C7xQ8).3S3	336,104
(C₇×Q₈).₄S₃ = C₇×C₃⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out C₇×Q₈	336	4	(C7xQ8).4S3	336,88

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