Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₇×Q₈

Direct product G=N×Q with N=C₂³ and Q=C₇×Q₈

		d	ρ	Label	ID
Q₈×C₂²×C₁₄		448		Q8xC2^2xC14	448,1387

Semidirect products G=N:Q with N=C₂³ and Q=C₇×Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₇×Q₈) = Q₈×F₈	φ: C₇×Q₈/Q₈ → C₇ ⊆ Aut C₂³	56	14-	C2^3:(C7xQ8)	448,1364
C₂³⋊₂(C₇×Q₈) = C₇×C₂³⋊Q₈	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3:2(C7xQ8)	448,801
C₂³⋊₃(C₇×Q₈) = C₇×C₂³⋊₂Q₈	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	112		C2^3:3(C7xQ8)	448,1326
C₂³⋊₄(C₇×Q₈) = C₁₄×C₂²⋊Q₈	φ: C₇×Q₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3:4(C7xQ8)	448,1306

Non-split extensions G=N.Q with N=C₂³ and Q=C₇×Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₇×Q₈) = C₇×C₄.₁₀C₄²	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	112	4	C2^3.1(C7xQ8)	448,142
C₂³.₂(C₇×Q₈) = C₇×C₂³.₉D₄	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	112		C2^3.2(C7xQ8)	448,146
C₂³.₃(C₇×Q₈) = C₇×C₂³.Q₈	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.3(C7xQ8)	448,804
C₂³.₄(C₇×Q₈) = C₇×C₂³.₄Q₈	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.4(C7xQ8)	448,807
C₂³.₅(C₇×Q₈) = C₇×M₄(2).C₄	φ: C₇×Q₈/C₁₄ → C₂² ⊆ Aut C₂³	112	4	C2^3.5(C7xQ8)	448,838
C₂³.₆(C₇×Q₈) = C₇×C₄.C₄²	φ: C₇×Q₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.6(C7xQ8)	448,145
C₂³.₇(C₇×Q₈) = C₇×C₂³.₇Q₈	φ: C₇×Q₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.7(C7xQ8)	448,788
C₂³.₈(C₇×Q₈) = C₇×C₂³.₈Q₈	φ: C₇×Q₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.8(C7xQ8)	448,793
C₂³.₉(C₇×Q₈) = C₁₄×C₈.C₄	φ: C₇×Q₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.9(C7xQ8)	448,837
C₂³.₁₀(C₇×Q₈) = C₁₄×C₂.C₄²	central extension (φ=1)	448		C2^3.10(C7xQ8)	448,783
C₂³.₁₁(C₇×Q₈) = C₄⋊C₄×C₂×C₁₄	central extension (φ=1)	448		C2^3.11(C7xQ8)	448,1296

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