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

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

		d	ρ	Label	ID
C₂×C₄×He₃⋊C₂		72		C2xC4xHe3:C2	432,385

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃⋊C₂)⋊₁C₂ = C₁₂.₉₁S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2):1C2	432,297
(C₄×He₃⋊C₂)⋊₂C₂ = C₁₂.₈₄S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2):2C2	432,296
(C₄×He₃⋊C₂)⋊₃C₂ = C₁₂.₈₆S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	36	6+	(C4xHe3:C2):3C2	432,302
(C₄×He₃⋊C₂)⋊₄C₂ = D₄×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	36	6	(C4xHe3:C2):4C2	432,390
(C₄×He₃⋊C₂)⋊₅C₂ = C₆².₁₆D₆	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2):5C2	432,391
(C₄×He₃⋊C₂)⋊₆C₂ = He₃⋊₅D₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2):6C2	432,395
(C₄×He₃⋊C₂)⋊₇C₂ = C₄×C₃²⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	36	6	(C4xHe3:C2):7C2	432,300
(C₄×He₃⋊C₂)⋊₈C₂ = C₆².₄₇D₆	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2):8C2	432,387

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃⋊C₂).₁C₂ = He₃⋊₃M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).1C2	432,82
(C₄×He₃⋊C₂).₂C₂ = C₁₂.₈₅S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6-	(C4xHe3:C2).2C2	432,298
(C₄×He₃⋊C₂).₃C₂ = Q₈×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).3C2	432,394
(C₄×He₃⋊C₂).₄C₂ = C₁₂.₈₉S₃²	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).4C2	432,81
(C₄×He₃⋊C₂).₅C₂ = He₃⋊₂(C₂×C₈)	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	3	(C4xHe3:C2).5C2	432,273
(C₄×He₃⋊C₂).₆C₂ = C₄×He₃⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	3	(C4xHe3:C2).6C2	432,275
(C₄×He₃⋊C₂).₇C₂ = He₃⋊₆M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).7C2	432,174
(C₄×He₃⋊C₂).₈C₂ = He₃⋊₁M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).8C2	432,274
(C₄×He₃⋊C₂).₉C₂ = C₄⋊(He₃⋊C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₄×He₃⋊C₂	72	6	(C4xHe3:C2).9C2	432,276
(C₄×He₃⋊C₂).₁₀C₂ = C₈×He₃⋊C₂	φ: trivial image	72	3	(C4xHe3:C2).10C2	432,173

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