Extensions 1→N→G→Q→1 with N=D₅₆⋊₇C₂ and Q=C₂

Direct product G=N×Q with N=D₅₆⋊₇C₂ and Q=C₂

		d	ρ	Label	ID
C₂×D₅₆⋊₇C₂		224		C2xD56:7C2	448,1194

Semidirect products G=N:Q with N=D₅₆⋊₇C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆⋊₇C₂⋊₁C₂ = D₁₁₂⋊₇C₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	2	D56:7C2:1C2	448,438
D₅₆⋊₇C₂⋊₂C₂ = D₈.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:2C2	448,681
D₅₆⋊₇C₂⋊₃C₂ = D₈⋊₁₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:3C2	448,1210
D₅₆⋊₇C₂⋊₄C₂ = D₂₈.₃₀D₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4	D56:7C2:4C2	448,1219
D₅₆⋊₇C₂⋊₅C₂ = C₅₆.₃₀C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4	D56:7C2:5C2	448,728
D₅₆⋊₇C₂⋊₆C₂ = D₇×C₄○D₈	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:6C2	448,1220
D₅₆⋊₇C₂⋊₇C₂ = D₈⋊₁₀D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:7C2	448,1221
D₅₆⋊₇C₂⋊₈C₂ = D₂₈.₂₉D₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:8C2	448,1215
D₅₆⋊₇C₂⋊₉C₂ = C₁₆⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4+	D56:7C2:9C2	448,442
D₅₆⋊₇C₂⋊₁₀C₂ = C₅₆.₉C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:10C2	448,1201
D₅₆⋊₇C₂⋊₁₁C₂ = D₄.₁₁D₂₈	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2:11C2	448,1204
D₅₆⋊₇C₂⋊₁₂C₂ = D₄.₁₂D₂₈	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4+	D56:7C2:12C2	448,1205
D₅₆⋊₇C₂⋊₁₃C₂ = D₄.₁₃D₂₈	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4-	D56:7C2:13C2	448,1206

Non-split extensions G=N.Q with N=D₅₆⋊₇C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆⋊₇C₂.₁C₂ = D₅₆.₁C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	2	D56:7C2.1C2	448,67
D₅₆⋊₇C₂.₂C₂ = Q₁₆.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4	D56:7C2.2C2	448,713
D₅₆⋊₇C₂.₃C₂ = Dic₂₈.C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4	D56:7C2.3C2	448,54
D₅₆⋊₇C₂.₄C₂ = D₅₆⋊₁₀C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2.4C2	448,428
D₅₆⋊₇C₂.₅C₂ = D₅₆⋊₇C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2.5C2	448,429
D₅₆⋊₇C₂.₆C₂ = D₅₆⋊₈C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2.6C2	448,45
D₅₆⋊₇C₂.₇C₂ = D₅₆⋊₂C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2.7C2	448,75
D₅₆⋊₇C₂.₈C₂ = D₅₆⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	112	4	D56:7C2.8C2	448,251
D₅₆⋊₇C₂.₉C₂ = C₁₆.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆⋊₇C₂	224	4-	D56:7C2.9C2	448,443
D₅₆⋊₇C₂.₁₀C₂ = D₅₆⋊₁₁C₄	φ: trivial image	112	2	D56:7C2.10C2	448,234

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