Extensions 1→N→G→Q→1 with N=C₃²×M₄(2) and Q=C₂

Direct product G=N×Q with N=C₃²×M₄(2) and Q=C₂

		d	ρ	Label	ID
M₄(2)×C₃×C₆		144		M4(2)xC3xC6	288,827

Semidirect products G=N:Q with N=C₃²×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃²×M₄(2))⋊₁C₂ = C₃×C₈⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):1C2	288,679
(C₃²×M₄(2))⋊₂C₂ = C₃×C₈.D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):2C2	288,680
(C₃²×M₄(2))⋊₃C₂ = C₂₄⋊₃D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):3C2	288,765
(C₃²×M₄(2))⋊₄C₂ = C₂₄.₅D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)):4C2	288,766
(C₃²×M₄(2))⋊₅C₂ = C₃²×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):5C2	288,833
(C₃²×M₄(2))⋊₆C₂ = C₃²×C₈.C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)):6C2	288,834
(C₃²×M₄(2))⋊₇C₂ = C₃×S₃×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):7C2	288,677
(C₃²×M₄(2))⋊₈C₂ = C₃×D₁₂.C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):8C2	288,678
(C₃²×M₄(2))⋊₉C₂ = M₄(2)×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):9C2	288,763
(C₃²×M₄(2))⋊₁₀C₂ = C₂₄.₄₇D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)):10C2	288,764
(C₃²×M₄(2))⋊₁₁C₂ = C₃×C₁₂.₄₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):11C2	288,257
(C₃²×M₄(2))⋊₁₂C₂ = C₃×D₁₂⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)):12C2	288,259
(C₃²×M₄(2))⋊₁₃C₂ = C₁₂.₁₉D₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):13C2	288,298
(C₃²×M₄(2))⋊₁₄C₂ = C₆².₃₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):14C2	288,300
(C₃²×M₄(2))⋊₁₅C₂ = C₃²×C₄.D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):15C2	288,318
(C₃²×M₄(2))⋊₁₆C₂ = C₃²×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	72		(C3^2xM4(2)):16C2	288,322
(C₃²×M₄(2))⋊₁₇C₂ = C₃²×C₈○D₄	φ: trivial image	144		(C3^2xM4(2)):17C2	288,828

Non-split extensions G=N.Q with N=C₃²×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃²×M₄(2)).₁C₂ = C₃×C₁₂.₅₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)).1C2	288,256
(C₃²×M₄(2)).₂C₂ = C₃×C₁₂.₄₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	48	4	(C3^2xM4(2)).2C2	288,258
(C₃²×M₄(2)).₃C₂ = C₆².₈Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)).3C2	288,297
(C₃²×M₄(2)).₄C₂ = C₁₂.₂₀D₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)).4C2	288,299
(C₃²×M₄(2)).₅C₂ = C₃²×C₄.₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)).5C2	288,319
(C₃²×M₄(2)).₆C₂ = C₃²×C₈.C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃²×M₄(2)	144		(C3^2xM4(2)).6C2	288,326

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