Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=Q₈

Direct product G=N×Q with N=C₂⁴ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₂⁴		128		Q8xC2^4	128,2321

Semidirect products G=N:Q with N=C₂⁴ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊Q₈ = C₂⁴⋊Q₈	φ: Q₈/C₁ → Q₈ ⊆ Aut C₂⁴	16	8+	C2^4:Q8	128,764
C₂⁴⋊₂Q₈ = C₂⁴⋊₂Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	16		C2^4:2Q8	128,761
C₂⁴⋊₃Q₈ = C₂×C₂³⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	64		C2^4:3Q8	128,1117
C₂⁴⋊₄Q₈ = C₂⁴⋊₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4:4Q8	128,1169
C₂⁴⋊₅Q₈ = C₂⁴⋊₅Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4:5Q8	128,1358
C₂⁴⋊₆Q₈ = C₂⁴⋊₆Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4:6Q8	128,1572
C₂⁴⋊₇Q₈ = C₂×C₂³⋊₂Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4:7Q8	128,2188
C₂⁴⋊₈Q₈ = C₂⁴⋊₈Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	32		C2^4:8Q8	128,1580
C₂⁴⋊₉Q₈ = C₂²×C₂²⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4:9Q8	128,2165

Non-split extensions G=N.Q with N=C₂⁴ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.Q₈ = C₂⁴.Q₈	φ: Q₈/C₁ → Q₈ ⊆ Aut C₂⁴	16	8+	C2^4.Q8	128,801
C₂⁴.₂Q₈ = C₂⁴.₂Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.2Q8	128,25
C₂⁴.₃Q₈ = C₂⁴.₃Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.3Q8	128,30
C₂⁴.₄Q₈ = C₂⁴.₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	16		C2^4.4Q8	128,36
C₂⁴.₅Q₈ = C₂⁴.₅Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	64		C2^4.5Q8	128,171
C₂⁴.₆Q₈ = C₂×C₄.₁₀C₄²	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.6Q8	128,463
C₂⁴.₇Q₈ = C₂⁴.₇Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.7Q8	128,470
C₂⁴.₈Q₈ = C₂×C₂³.₉D₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.8Q8	128,471
C₂⁴.₉Q₈ = C₂⁴.₉Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.9Q8	128,543
C₂⁴.₁₀Q₈ = C₂⁴.₁₀Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.10Q8	128,587
C₂⁴.₁₁Q₈ = C₂⁴.₁₁Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	16	4	C2^4.11Q8	128,823
C₂⁴.₁₂Q₈ = C₂⁴.₉₁D₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.12Q8	128,1047
C₂⁴.₁₃Q₈ = C₂×C₂³.Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	64		C2^4.13Q8	128,1121
C₂⁴.₁₄Q₈ = C₂×C₂³.₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	64		C2^4.14Q8	128,1125
C₂⁴.₁₅Q₈ = C₂⁴.₁₅Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.15Q8	128,1574
C₂⁴.₁₆Q₈ = C₂×M₄(2).C₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₂⁴	32		C2^4.16Q8	128,1647
C₂⁴.₁₇Q₈ = C₂⁴.₁₇Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4.17Q8	128,165
C₂⁴.₁₈Q₈ = C₂×C₄.C₄²	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4.18Q8	128,469
C₂⁴.₁₉Q₈ = C₂⁴.₁₉Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	32		C2^4.19Q8	128,542
C₂⁴.₂₀Q₈ = C₂×C₂³.₇Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4.20Q8	128,1010
C₂⁴.₂₁Q₈ = C₂×C₂³.₈Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4.21Q8	128,1018
C₂⁴.₂₂Q₈ = C₂²×C₈.C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂⁴	64		C2^4.22Q8	128,1646
C₂⁴.₂₃Q₈ = C₂²×C₂.C₄²	central extension (φ=1)	128		C2^4.23Q8	128,998
C₂⁴.₂₄Q₈ = C₂³×C₄⋊C₄	central extension (φ=1)	128		C2^4.24Q8	128,2152

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Extensions 1→N→G→Q→1 with N=C24 and Q=Q8

Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=Q₈