Extensions 1→N→G→Q→1 with N=C₂²×He₃ and Q=C₂

Direct product G=N×Q with N=C₂²×He₃ and Q=C₂

		d	ρ	Label	ID
C₂³×He₃		72		C2^3xHe3	216,115

Semidirect products G=N:Q with N=C₂²×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃)⋊₁C₂ = D₄×He₃	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):1C2	216,77
(C₂²×He₃)⋊₂C₂ = He₃⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):2C2	216,60
(C₂²×He₃)⋊₃C₂ = He₃⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):3C2	216,72
(C₂²×He₃)⋊₄C₂ = C₂²×C₃²⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	36		(C2^2xHe3):4C2	216,110
(C₂²×He₃)⋊₅C₂ = C₂²×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	36		(C2^2xHe3):5C2	216,113

Non-split extensions G=N.Q with N=C₂²×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃).₁C₂ = C₂×C₃²⋊C₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).1C2	216,59
(C₂²×He₃).₂C₂ = C₂×He₃⋊₃C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).2C2	216,71
(C₂²×He₃).₃C₂ = C₂×C₄×He₃	φ: trivial image	72		(C2^2xHe3).3C2	216,74

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