Extensions 1→N→G→Q→1 with N=C₃²×C₁₂ and Q=C₂

Direct product G=N×Q with N=C₃²×C₁₂ and Q=C₂

		d	ρ	Label	ID
C₃×C₆×C₁₂		216		C3xC6xC12	216,150

Semidirect products G=N:Q with N=C₃²×C₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃²×C₁₂)⋊₁C₂ = C₃³⋊₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	108		(C3^2xC12):1C2	216,147
(C₃²×C₁₂)⋊₂C₂ = C₃²×D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12):2C2	216,137
(C₃²×C₁₂)⋊₃C₂ = C₃×C₁₂⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12):3C2	216,142
(C₃²×C₁₂)⋊₄C₂ = S₃×C₃×C₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12):4C2	216,136
(C₃²×C₁₂)⋊₅C₂ = C₁₂×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12):5C2	216,141
(C₃²×C₁₂)⋊₆C₂ = C₄×C₃³⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	108		(C3^2xC12):6C2	216,146
(C₃²×C₁₂)⋊₇C₂ = D₄×C₃³	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	108		(C3^2xC12):7C2	216,151

Non-split extensions G=N.Q with N=C₃²×C₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃²×C₁₂).₁C₂ = C₃³⋊₈Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	216		(C3^2xC12).1C2	216,145
(C₃²×C₁₂).₂C₂ = C₃²×Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12).2C2	216,135
(C₃²×C₁₂).₃C₂ = C₃×C₃²⋊₄Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12).3C2	216,140
(C₃²×C₁₂).₄C₂ = C₃²×C₃⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12).4C2	216,82
(C₃²×C₁₂).₅C₂ = C₃×C₃²⋊₄C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	72		(C3^2xC12).5C2	216,83
(C₃²×C₁₂).₆C₂ = C₃³⋊₇C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	216		(C3^2xC12).6C2	216,84
(C₃²×C₁₂).₇C₂ = Q₈×C₃³	φ: C₂/C₁ → C₂ ⊆ Aut C₃²×C₁₂	216		(C3^2xC12).7C2	216,152

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