Extensions 1→N→G→Q→1 with N=C₂×C₆ and Q=S₃

Direct product G=N×Q with N=C₂×C₆ and Q=S₃

		d	ρ	Label	ID
S₃×C₂×C₆		24		S3xC2xC6	72,48

Semidirect products G=N:Q with N=C₂×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆)⋊₁S₃ = C₃×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₆	12	3	(C2xC6):1S3	72,42
(C₂×C₆)⋊₂S₃ = C₃⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₆	12	6+	(C2xC6):2S3	72,43
(C₂×C₆)⋊₃S₃ = C₃×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	12	2	(C2xC6):3S3	72,30
(C₂×C₆)⋊₄S₃ = C₃²⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	36		(C2xC6):4S3	72,35
(C₂×C₆)⋊₅S₃ = C₂²×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	36		(C2xC6):5S3	72,49

Non-split extensions G=N.Q with N=C₂×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆).S₃ = C₃.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₆	18	6+	(C2xC6).S3	72,15
(C₂×C₆).₂S₃ = C₂×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	72		(C2xC6).2S3	72,7
(C₂×C₆).₃S₃ = C₉⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	36	2	(C2xC6).3S3	72,8
(C₂×C₆).₄S₃ = C₂²×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	36		(C2xC6).4S3	72,17
(C₂×C₆).₅S₃ = C₂×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₆	72		(C2xC6).5S3	72,34
(C₂×C₆).₆S₃ = C₆×Dic₃	central extension (φ=1)	24		(C2xC6).6S3	72,29

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