Extensions 1→N→G→Q→1 with N=C₂²⋊C₄ and Q=C₃×C₆

Direct product G=N×Q with N=C₂²⋊C₄ and Q=C₃×C₆

		d	ρ	Label	ID
C₂²⋊C₄×C₃×C₆		144		C2^2:C4xC3xC6	288,812

Semidirect products G=N:Q with N=C₂²⋊C₄ and Q=C₃×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄⋊₁(C₃×C₆) = C₃²×C₂³⋊C₄	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	72		C2^2:C4:1(C3xC6)	288,317
C₂²⋊C₄⋊₂(C₃×C₆) = C₃²×C₂²≀C₂	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	72		C2^2:C4:2(C3xC6)	288,817
C₂²⋊C₄⋊₃(C₃×C₆) = C₃²×C₄⋊D₄	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	144		C2^2:C4:3(C3xC6)	288,818
C₂²⋊C₄⋊₄(C₃×C₆) = C₃²×C₂².D₄	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	144		C2^2:C4:4(C3xC6)	288,820
C₂²⋊C₄⋊₅(C₃×C₆) = C₃²×C₄.₄D₄	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	144		C2^2:C4:5(C3xC6)	288,821
C₂²⋊C₄⋊₆(C₃×C₆) = D₄×C₃×C₁₂	φ: trivial image	144		C2^2:C4:6(C3xC6)	288,815

Non-split extensions G=N.Q with N=C₂²⋊C₄ and Q=C₃×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄.₁(C₃×C₆) = C₃²×C₂²⋊Q₈	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	144		C2^2:C4.1(C3xC6)	288,819
C₂²⋊C₄.₂(C₃×C₆) = C₃²×C₄²⋊₂C₂	φ: C₃×C₆/C₃² → C₂ ⊆ Out C₂²⋊C₄	144		C2^2:C4.2(C3xC6)	288,823
C₂²⋊C₄.₃(C₃×C₆) = C₃²×C₄²⋊C₂	φ: trivial image	144		C2^2:C4.3(C3xC6)	288,814

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