Extensions 1→N→G→Q→1 with N=C₂²×C₃²⋊C₆ and Q=C₂

Direct product G=N×Q with N=C₂²×C₃²⋊C₆ and Q=C₂

		d	ρ	Label	ID
C₂³×C₃²⋊C₆		72		C2^3xC3^2:C6	432,558

Semidirect products G=N:Q with N=C₂²×C₃²⋊C₆ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×C₃²⋊C₆)⋊₁C₂ = C₂×He₃⋊₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6):1C2	432,320
(C₂²×C₃²⋊C₆)⋊₂C₂ = C₂×He₃⋊₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6):2C2	432,322
(C₂²×C₃²⋊C₆)⋊₃C₂ = C₆²⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	36	12+	(C2^2xC3^2:C6):3C2	432,323
(C₂²×C₃²⋊C₆)⋊₄C₂ = C₂×He₃⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6):4C2	432,350
(C₂²×C₃²⋊C₆)⋊₅C₂ = D₄×C₃²⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	36	12+	(C2^2xC3^2:C6):5C2	432,360
(C₂²×C₃²⋊C₆)⋊₆C₂ = C₂×He₃⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6):6C2	432,377
(C₂²×C₃²⋊C₆)⋊₇C₂ = C₂²×C₃²⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	36		(C2^2xC3^2:C6):7C2	432,545

Non-split extensions G=N.Q with N=C₂²×C₃²⋊C₆ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×C₃²⋊C₆).₁C₂ = C₆².₄D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6).1C2	432,97
(C₂²×C₃²⋊C₆).₂C₂ = C₆².₂₁D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6).2C2	432,141
(C₂²×C₃²⋊C₆).₃C₂ = C₂×C₆.S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₂²×C₃²⋊C₆	72		(C2^2xC3^2:C6).3C2	432,317
(C₂²×C₃²⋊C₆).₄C₂ = C₂×C₄×C₃²⋊C₆	φ: trivial image	72		(C2^2xC3^2:C6).4C2	432,349

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