Extensions 1→N→G→Q→1 with N=He₃ and Q=C₂×C₆

Direct product G=N×Q with N=He₃ and Q=C₂×C₆

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

Semidirect products G=N:Q with N=He₃ and Q=C₂×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊(C₂×C₆) = C₂×C₃≀S₃	φ: C₂×C₆/C₂ → C₆ ⊆ Out He₃	18	3	He3:(C2xC6)	324,68
He₃⋊₂(C₂×C₆) = C₃×C₃²⋊D₆	φ: C₂×C₆/C₃ → C₂² ⊆ Out He₃	18	6	He3:2(C2xC6)	324,117
He₃⋊₃(C₂×C₆) = C₂²×C₃≀C₃	φ: C₂×C₆/C₂² → C₃ ⊆ Out He₃	36		He3:3(C2xC6)	324,86
He₃⋊₄(C₂×C₆) = C₂²×He₃⋊C₃	φ: C₂×C₆/C₂² → C₃ ⊆ Out He₃	108		He3:4(C2xC6)	324,88
He₃⋊₅(C₂×C₆) = C₆×C₃²⋊C₆	φ: C₂×C₆/C₆ → C₂ ⊆ Out He₃	36	6	He3:5(C2xC6)	324,138
He₃⋊₆(C₂×C₆) = C₆×He₃⋊C₂	φ: C₂×C₆/C₆ → C₂ ⊆ Out He₃	54		He3:6(C2xC6)	324,145

Non-split extensions G=N.Q with N=He₃ and Q=C₂×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁(C₂×C₆) = C₂×He₃.C₆	φ: C₂×C₆/C₂ → C₆ ⊆ Out He₃	54	3	He3.1(C2xC6)	324,70
He₃.₂(C₂×C₆) = C₂×He₃.₂C₆	φ: C₂×C₆/C₂ → C₆ ⊆ Out He₃	54	3	He3.2(C2xC6)	324,72
He₃.₃(C₂×C₆) = C₂²×He₃.C₃	φ: C₂×C₆/C₂² → C₃ ⊆ Out He₃	108		He3.3(C2xC6)	324,87
He₃.₄(C₂×C₆) = C₂×He₃.₄C₆	φ: C₂×C₆/C₆ → C₂ ⊆ Out He₃	54	3	He3.4(C2xC6)	324,148
He₃.₅(C₂×C₆) = C₂²×C₉○He₃	φ: trivial image	108		He3.5(C2xC6)	324,154

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