Extensions 1→N→G→Q→1 with N=He₃⋊₄C₈ and Q=C₂

Direct product G=N×Q with N=He₃⋊₄C₈ and Q=C₂

		d	ρ	Label	ID
C₂×He₃⋊₄C₈		144		C2xHe3:4C8	432,184

Semidirect products G=N:Q with N=He₃⋊₄C₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₄C₈⋊₁C₂ = He₃⋊₂D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6+	He3:4C8:1C2	432,79
He₃⋊₄C₈⋊₂C₂ = He₃⋊₃SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:2C2	432,78
He₃⋊₄C₈⋊₃C₂ = He₃⋊₇D₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:3C2	432,192
He₃⋊₄C₈⋊₄C₂ = C₃²⋊C₆⋊C₈	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:4C2	432,76
He₃⋊₄C₈⋊₅C₂ = He₃⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:5C2	432,77
He₃⋊₄C₈⋊₆C₂ = He₃⋊₉SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:6C2	432,193
He₃⋊₄C₈⋊₇C₂ = He₃⋊₁₁SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:7C2	432,196
He₃⋊₄C₈⋊₈C₂ = He₃⋊₆M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:8C2	432,174
He₃⋊₄C₈⋊₉C₂ = He₃⋊₈M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	72	6	He3:4C8:9C2	432,185
He₃⋊₄C₈⋊₁₀C₂ = C₈×He₃⋊C₂	φ: trivial image	72	3	He3:4C8:10C2	432,173

Non-split extensions G=N.Q with N=He₃⋊₄C₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₄C₈.₁C₂ = He₃⋊₂C₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	144	3	He3:4C8.1C2	432,57
He₃⋊₄C₈.₂C₂ = He₃⋊₂Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	144	6-	He3:4C8.2C2	432,80
He₃⋊₄C₈.₃C₂ = He₃⋊₇Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out He₃⋊₄C₈	144	6	He3:4C8.3C2	432,197

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