Extensions 1→N→G→Q→1 with N=C₂²×He₃ and Q=C₃

Direct product G=N×Q with N=C₂²×He₃ and Q=C₃

		d	ρ	Label	ID
C₂×C₆×He₃		108		C2xC6xHe3	324,152

Semidirect products G=N:Q with N=C₂²×He₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃)⋊₁C₃ = He₃⋊A₄	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	54	9	(C2^2xHe3):1C3	324,54
(C₂²×He₃)⋊₂C₃ = He₃⋊₂A₄	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	36	9	(C2^2xHe3):2C3	324,55
(C₂²×He₃)⋊₃C₃ = C₂²×C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	36		(C2^2xHe3):3C3	324,86
(C₂²×He₃)⋊₄C₃ = C₂²×He₃⋊C₃	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	108		(C2^2xHe3):4C3	324,88
(C₂²×He₃)⋊₅C₃ = A₄×He₃	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	36	9	(C2^2xHe3):5C3	324,130

Non-split extensions G=N.Q with N=C₂²×He₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃).₁C₃ = He₃.A₄	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	54	9	(C2^2xHe3).1C3	324,53
(C₂²×He₃).₂C₃ = C₂²×He₃.C₃	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	108		(C2^2xHe3).2C3	324,87
(C₂²×He₃).₃C₃ = He₃.₂A₄	φ: C₃/C₁ → C₃ ⊆ Out C₂²×He₃	54	9	(C2^2xHe3).3C3	324,129
(C₂²×He₃).₄C₃ = C₂²×C₉○He₃	φ: trivial image	108		(C2^2xHe3).4C3	324,154

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