Extensions 1→N→G→Q→1 with N=He₃⋊₄D₄ and Q=C₂

Direct product G=N×Q with N=He₃⋊₄D₄ and Q=C₂

		d	ρ	Label	ID
C₂×He₃⋊₄D₄		72		C2xHe3:4D4	432,350

Semidirect products G=N:Q with N=He₃⋊₄D₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₄D₄⋊₁C₂ = He₃⋊₂D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	6+	He3:4D4:1C2	432,79
He₃⋊₄D₄⋊₂C₂ = He₃⋊₃D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4:2C2	432,83
He₃⋊₄D₄⋊₃C₂ = He₃⋊₆D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4:3C2	432,153
He₃⋊₄D₄⋊₄C₂ = C₁₂⋊S₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4:4C2	432,295
He₃⋊₄D₄⋊₅C₂ = C₁₂.₈₄S₃²	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	6	He3:4D4:5C2	432,296
He₃⋊₄D₄⋊₆C₂ = C₃⋊S₃⋊D₁₂	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	36	12+	He3:4D4:6C2	432,301
He₃⋊₄D₄⋊₇C₂ = C₁₂.₈₆S₃²	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	36	6+	He3:4D4:7C2	432,302
He₃⋊₄D₄⋊₈C₂ = D₄×C₃²⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	36	12+	He3:4D4:8C2	432,360
He₃⋊₄D₄⋊₉C₂ = (Q₈×He₃)⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4:9C2	432,369
He₃⋊₄D₄⋊₁₀C₂ = He₃⋊₄D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	6+	He3:4D4:10C2	432,118
He₃⋊₄D₄⋊₁₁C₂ = C₆².₃₆D₆	φ: trivial image	72	6	He3:4D4:11C2	432,351

Non-split extensions G=N.Q with N=He₃⋊₄D₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₄D₄.₁C₂ = He₃⋊₃SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	6	He3:4D4.1C2	432,78
He₃⋊₄D₄.₂C₂ = He₃⋊₅SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4.2C2	432,85
He₃⋊₄D₄.₃C₂ = He₃⋊₁₀SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	12+	He3:4D4.3C2	432,161
He₃⋊₄D₄.₄C₂ = He₃⋊₆SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄D₄	72	6	He3:4D4.4C2	432,117

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁