Extensions 1→N→G→Q→1 with N=He₃⋊(C₂×C₄) and Q=C₂

Direct product G=N×Q with N=He₃⋊(C₂×C₄) and Q=C₂

		d	ρ	Label	ID
C₂×He₃⋊(C₂×C₄)		72		C2xHe3:(C2xC4)	432,321

Semidirect products G=N:Q with N=He₃⋊(C₂×C₄) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊(C₂×C₄)⋊₁C₂ = C₁₂.S₃²	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	72	12-	He3:(C2xC4):1C2	432,299
He₃⋊(C₂×C₄)⋊₂C₂ = C₆².₈D₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	72	12-	He3:(C2xC4):2C2	432,318
He₃⋊(C₂×C₄)⋊₃C₂ = C₆²⋊₂D₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	36	6	He3:(C2xC4):3C2	432,324
He₃⋊(C₂×C₄)⋊₄C₂ = C₃²⋊D₆⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	36	6	He3:(C2xC4):4C2	432,238
He₃⋊(C₂×C₄)⋊₅C₂ = C₄×C₃²⋊D₆	φ: trivial image	36	6	He3:(C2xC4):5C2	432,300

Non-split extensions G=N.Q with N=He₃⋊(C₂×C₄) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊(C₂×C₄).₁C₂ = C₁₂.₈₅S₃²	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	72	6-	He3:(C2xC4).1C2	432,298
He₃⋊(C₂×C₄).₂C₂ = C₆.S₃≀C₂	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊(C₂×C₄)	72	6-	He3:(C2xC4).2C2	432,237

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