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

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

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

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊(S₃×C₇) = C₇×GL₂(𝔽₃)	φ: S₃×C₇/C₇ → S₃ ⊆ Out Q₈	56	2	Q8:(S3xC7)	336,116
Q₈⋊₂(S₃×C₇) = C₇×Q₈⋊₂S₃	φ: S₃×C₇/C₂₁ → C₂ ⊆ Out Q₈	168	4	Q8:2(S3xC7)	336,87
Q₈⋊₃(S₃×C₇) = C₇×Q₈⋊₃S₃	φ: trivial image	168	4	Q8:3(S3xC7)	336,191

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(S₃×C₇) = C₇×CSU₂(𝔽₃)	φ: S₃×C₇/C₇ → S₃ ⊆ Out Q₈	112	2	Q8.(S3xC7)	336,115
Q₈.₂(S₃×C₇) = C₇×C₃⋊Q₁₆	φ: S₃×C₇/C₂₁ → C₂ ⊆ Out Q₈	336	4	Q8.2(S3xC7)	336,88

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