Extensions 1→N→G→Q→1 with N=C₂²×A₄ and Q=S₃

Direct product G=N×Q with N=C₂²×A₄ and Q=S₃

		d	ρ	Label	ID
C₂²×S₃×A₄		36		C2^2xS3xA4	288,1037

Semidirect products G=N:Q with N=C₂²×A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×A₄)⋊₁S₃ = A₄×S₄	φ: S₃/C₁ → S₃ ⊆ Out C₂²×A₄	16	9+	(C2^2xA4):1S3	288,1024
(C₂²×A₄)⋊₂S₃ = PSO₄⁺ (𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₂²×A₄	12	9+	(C2^2xA4):2S3	288,1026
(C₂²×A₄)⋊₃S₃ = A₄×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂²×A₄	36	6	(C2^2xA4):3S3	288,928
(C₂²×A₄)⋊₄S₃ = (C₂×C₆)⋊₄S₄	φ: S₃/C₃ → C₂ ⊆ Out C₂²×A₄	36	6	(C2^2xA4):4S3	288,917
(C₂²×A₄)⋊₅S₃ = C₂²×C₃⋊S₄	φ: S₃/C₃ → C₂ ⊆ Out C₂²×A₄	36		(C2^2xA4):5S3	288,1034

Non-split extensions G=N.Q with N=C₂²×A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×A₄).S₃ = C₂×C₆.₇S₄	φ: S₃/C₃ → C₂ ⊆ Out C₂²×A₄	72		(C2^2xA4).S3	288,916
(C₂²×A₄).₂S₃ = C₂×Dic₃×A₄	φ: trivial image	72		(C2^2xA4).2S3	288,927

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