Extensions 1→N→G→Q→1 with N=D₄×He₃ and Q=C₂

Direct product G=N×Q with N=D₄×He₃ and Q=C₂

		d	ρ	Label	ID
C₂×D₄×He₃		72		C2xD4xHe3	432,404

Semidirect products G=N:Q with N=D₄×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×He₃)⋊₁C₂ = He₃⋊₆D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	12+	(D4xHe3):1C2	432,153
(D₄×He₃)⋊₂C₂ = He₃⋊₇D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	6	(D4xHe3):2C2	432,192
(D₄×He₃)⋊₃C₂ = D₄×C₃²⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	36	12+	(D4xHe3):3C2	432,360
(D₄×He₃)⋊₄C₂ = C₆².₁₃D₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	12-	(D4xHe3):4C2	432,361
(D₄×He₃)⋊₅C₂ = D₄×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	36	6	(D4xHe3):5C2	432,390
(D₄×He₃)⋊₆C₂ = C₆².₁₆D₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	6	(D4xHe3):6C2	432,391
(D₄×He₃)⋊₇C₂ = D₈×He₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	6	(D4xHe3):7C2	432,216
(D₄×He₃)⋊₈C₂ = C₄○D₄×He₃	φ: trivial image	72	6	(D4xHe3):8C2	432,410

Non-split extensions G=N.Q with N=D₄×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×He₃).₁C₂ = He₃⋊₈SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	12-	(D4xHe3).1C2	432,152
(D₄×He₃).₂C₂ = He₃⋊₉SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	6	(D4xHe3).2C2	432,193
(D₄×He₃).₃C₂ = SD₁₆×He₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×He₃	72	6	(D4xHe3).3C2	432,219

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