Extensions 1→N→G→Q→1 with N=C₇×C₈⋊C₂² and Q=C₂

Direct product G=N×Q with N=C₇×C₈⋊C₂² and Q=C₂

		d	ρ	Label	ID
C₁₄×C₈⋊C₂²		112		C14xC8:C2^2	448,1356

Semidirect products G=N:Q with N=C₇×C₈⋊C₂² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×C₈⋊C₂²)⋊₁C₂ = D₇×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	56	8+	(C7xC8:C2^2):1C2	448,1225
(C₇×C₈⋊C₂²)⋊₂C₂ = SD₁₆⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8-	(C7xC8:C2^2):2C2	448,1226
(C₇×C₈⋊C₂²)⋊₃C₂ = D₈⋊₅D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8+	(C7xC8:C2^2):3C2	448,1227
(C₇×C₈⋊C₂²)⋊₄C₂ = D₈⋊₆D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8-	(C7xC8:C2^2):4C2	448,1228
(C₇×C₈⋊C₂²)⋊₅C₂ = D₂₈⋊₁₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	56	8+	(C7xC8:C2^2):5C2	448,732
(C₇×C₈⋊C₂²)⋊₆C₂ = M₄(2).D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8+	(C7xC8:C2^2):6C2	448,733
(C₇×C₈⋊C₂²)⋊₇C₂ = D₂₈.₃₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8-	(C7xC8:C2^2):7C2	448,735
(C₇×C₈⋊C₂²)⋊₈C₂ = C₇×D₄⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	56	4	(C7xC8:C2^2):8C2	448,861
(C₇×C₈⋊C₂²)⋊₉C₂ = C₇×D₄.₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	4	(C7xC8:C2^2):9C2	448,862
(C₇×C₈⋊C₂²)⋊₁₀C₂ = C₇×D₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	4	(C7xC8:C2^2):10C2	448,880
(C₇×C₈⋊C₂²)⋊₁₁C₂ = C₇×D₄○D₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	4	(C7xC8:C2^2):11C2	448,1359
(C₇×C₈⋊C₂²)⋊₁₂C₂ = C₇×D₄○SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	4	(C7xC8:C2^2):12C2	448,1360
(C₇×C₈⋊C₂²)⋊₁₃C₂ = C₇×D₈⋊C₂²	φ: trivial image	112	4	(C7xC8:C2^2):13C2	448,1358

Non-split extensions G=N.Q with N=C₇×C₈⋊C₂² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×C₈⋊C₂²).₁C₂ = M₄(2).₁₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	8-	(C7xC8:C2^2).1C2	448,734
(C₇×C₈⋊C₂²).₂C₂ = C₇×D₄.₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×C₈⋊C₂²	112	4	(C7xC8:C2^2).2C2	448,879

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