Extensions 1→N→G→Q→1 with N=C₇⋊C₈ and Q=Q₈

Direct product G=N×Q with N=C₇⋊C₈ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₇⋊C₈		448		Q8xC7:C8	448,557

Semidirect products G=N:Q with N=C₇⋊C₈ and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊C₈⋊₁Q₈ = C₅₆⋊₃Q₈	φ: Q₈/C₂ → C₂² ⊆ Out C₇⋊C₈	448		C7:C8:1Q8	448,390
C₇⋊C₈⋊₂Q₈ = C₅₆⋊₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Out C₇⋊C₈	448		C7:C8:2Q8	448,410
C₇⋊C₈⋊₃Q₈ = C₄².₆₈D₁₄	φ: Q₈/C₂ → C₂² ⊆ Out C₇⋊C₈	448		C7:C8:3Q8	448,599
C₇⋊C₈⋊₄Q₈ = C₄².₇₆D₁₄	φ: Q₈/C₂ → C₂² ⊆ Out C₇⋊C₈	448		C7:C8:4Q8	448,614
C₇⋊C₈⋊₅Q₈ = C₅₆⋊₅Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:5Q8	448,389
C₇⋊C₈⋊₆Q₈ = C₅₆⋊₂Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:6Q8	448,408
C₇⋊C₈⋊₇Q₈ = C₂₈.₁₇D₈	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:7Q8	448,612
C₇⋊C₈⋊₈Q₈ = C₂₈.SD₁₆	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:8Q8	448,613
C₇⋊C₈⋊₉Q₈ = C₄².₂₇D₁₄	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:9Q8	448,362
C₇⋊C₈⋊₁₀Q₈ = C₂₈.M₄(2)	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:10Q8	448,365
C₇⋊C₈⋊₁₁Q₈ = C₄².₂₁₀D₁₄	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8:11Q8	448,558
C₇⋊C₈⋊₁₂Q₈ = Dic₁₄⋊C₈	φ: trivial image	448		C7:C8:12Q8	448,364

Non-split extensions G=N.Q with N=C₇⋊C₈ and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊C₈.₁Q₈ = C₅₆.₈Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8.1Q8	448,392
C₇⋊C₈.₂Q₈ = C₅₆.₄Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8.2Q8	448,412
C₇⋊C₈.₃Q₈ = C₄².₂₁₅D₁₄	φ: Q₈/C₄ → C₂ ⊆ Out C₇⋊C₈	448		C7:C8.3Q8	448,598

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁