Extensions 1→N→G→Q→1 with N=C₂×C₃⋊S₃ and Q=C₆

Direct product G=N×Q with N=C₂×C₃⋊S₃ and Q=C₆

		d	ρ	Label	ID
C₂×C₆×C₃⋊S₃		72		C2xC6xC3:S3	216,175

Semidirect products G=N:Q with N=C₂×C₃⋊S₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃⋊S₃)⋊₁C₆ = He₃⋊₄D₄	φ: C₆/C₁ → C₆ ⊆ Out C₂×C₃⋊S₃	36	6+	(C2xC3:S3):1C6	216,51
(C₂×C₃⋊S₃)⋊₂C₆ = He₃⋊₆D₄	φ: C₆/C₁ → C₆ ⊆ Out C₂×C₃⋊S₃	36	6	(C2xC3:S3):2C6	216,60
(C₂×C₃⋊S₃)⋊₃C₆ = C₂²×C₃²⋊C₆	φ: C₆/C₂ → C₃ ⊆ Out C₂×C₃⋊S₃	36		(C2xC3:S3):3C6	216,110
(C₂×C₃⋊S₃)⋊₄C₆ = C₃×C₃⋊D₁₂	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3):4C6	216,122
(C₂×C₃⋊S₃)⋊₅C₆ = C₃×C₁₂⋊S₃	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	72		(C2xC3:S3):5C6	216,142
(C₂×C₃⋊S₃)⋊₆C₆ = C₃×C₃²⋊₇D₄	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	36		(C2xC3:S3):6C6	216,144
(C₂×C₃⋊S₃)⋊₇C₆ = S₃²×C₆	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3):7C6	216,170

Non-split extensions G=N.Q with N=C₂×C₃⋊S₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃⋊S₃).C₆ = C₄×C₃²⋊C₆	φ: C₆/C₂ → C₃ ⊆ Out C₂×C₃⋊S₃	36	6	(C2xC3:S3).C6	216,50
(C₂×C₃⋊S₃).₂C₆ = C₃×C₆.D₆	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).2C6	216,120
(C₂×C₃⋊S₃).₃C₆ = C₆×C₃²⋊C₄	φ: C₆/C₃ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).3C6	216,168
(C₂×C₃⋊S₃).₄C₆ = C₁₂×C₃⋊S₃	φ: trivial image	72		(C2xC3:S3).4C6	216,141

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