Extensions 1→N→G→Q→1 with N=C₄.A₄ and Q=S₃

Direct product G=N×Q with N=C₄.A₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₄.A₄		48	4	S3xC4.A4	288,925

Semidirect products G=N:Q with N=C₄.A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₄⋊₁S₃ = C₁₂.₇S₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	48	4+	C4.A4:1S3	288,915
C₄.A₄⋊₂S₃ = C₁₂.₁₄S₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	48	4	C4.A4:2S3	288,914
C₄.A₄⋊₃S₃ = Dic₆.A₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	72	4+	C4.A4:3S3	288,924
C₄.A₄⋊₄S₃ = D₁₂.A₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	48	4-	C4.A4:4S3	288,926

Non-split extensions G=N.Q with N=C₄.A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₄.₁S₃ = C₁₂.₆S₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	96	4-	C4.A4.1S3	288,913
C₄.A₄.₂S₃ = C₃⋊U₂(𝔽₃)	φ: S₃/C₃ → C₂ ⊆ Out C₄.A₄	72	4	C4.A4.2S3	288,404
C₄.A₄.₃S₃ = SL₂(𝔽₃).Dic₃	φ: trivial image	96	4	C4.A4.3S3	288,410

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