Extensions 1→N→G→Q→1 with N=C₂²×C₃⋊S₃ and Q=C₂

Direct product G=N×Q with N=C₂²×C₃⋊S₃ and Q=C₂

		d	ρ	Label	ID
C₂³×C₃⋊S₃		72		C2^3xC3:S3	144,196

Semidirect products G=N:Q with N=C₂²×C₃⋊S₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×C₃⋊S₃)⋊₁C₂ = C₂×C₃⋊D₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	24		(C2^2xC3:S3):1C2	144,151
(C₂²×C₃⋊S₃)⋊₂C₂ = Dic₃⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	12	4+	(C2^2xC3:S3):2C2	144,154
(C₂²×C₃⋊S₃)⋊₃C₂ = C₂×C₁₂⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	72		(C2^2xC3:S3):3C2	144,170
(C₂²×C₃⋊S₃)⋊₄C₂ = D₄×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	36		(C2^2xC3:S3):4C2	144,172
(C₂²×C₃⋊S₃)⋊₅C₂ = C₂×C₃²⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	72		(C2^2xC3:S3):5C2	144,177
(C₂²×C₃⋊S₃)⋊₆C₂ = C₂²×S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	24		(C2^2xC3:S3):6C2	144,192

Non-split extensions G=N.Q with N=C₂²×C₃⋊S₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×C₃⋊S₃).₁C₂ = C₆.D₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	24		(C2^2xC3:S3).1C2	144,65
(C₂²×C₃⋊S₃).₂C₂ = C₆.₁₁D₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	72		(C2^2xC3:S3).2C2	144,95
(C₂²×C₃⋊S₃).₃C₂ = C₆²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	12	4+	(C2^2xC3:S3).3C2	144,136
(C₂²×C₃⋊S₃).₄C₂ = C₂×C₆.D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	24		(C2^2xC3:S3).4C2	144,149
(C₂²×C₃⋊S₃).₅C₂ = C₂²×C₃²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃⋊S₃	24		(C2^2xC3:S3).5C2	144,191
(C₂²×C₃⋊S₃).₆C₂ = C₂×C₄×C₃⋊S₃	φ: trivial image	72		(C2^2xC3:S3).6C2	144,169

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