Extensions 1→N→G→Q→1 with N=C₈ and Q=C₂⁴

Direct product G=N×Q with N=C₈ and Q=C₂⁴

		d	ρ	Label	ID
C₂⁴×C₈		128		C2^4xC8	128,2301

Semidirect products G=N:Q with N=C₈ and Q=C₂⁴

extension	φ:Q→Aut N	d	Label	ID
C₈⋊C₂⁴ = C₂²×C₈⋊C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32	C8:C2^4	128,2310
C₈⋊₂C₂⁴ = C₂³×D₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64	C8:2C2^4	128,2306
C₈⋊₃C₂⁴ = C₂³×SD₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64	C8:3C2^4	128,2307
C₈⋊₄C₂⁴ = C₂³×M₄(2)	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64	C8:4C2^4	128,2302

Non-split extensions G=N.Q with N=C₈ and Q=C₂⁴

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁C₂⁴ = C₂²×C₈.C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	64		C8.1C2^4	128,2311
C₈.₂C₂⁴ = C₂×D₈⋊C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32		C8.2C2^4	128,2312
C₈.₃C₂⁴ = C₂×D₄○D₈	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32		C8.3C2^4	128,2313
C₈.₄C₂⁴ = C₂×D₄○SD₁₆	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32		C8.4C2^4	128,2314
C₈.₅C₂⁴ = C₂×Q₈○D₈	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	64		C8.5C2^4	128,2315
C₈.₆C₂⁴ = C₈.C₂⁴	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32	4	C8.6C2^4	128,2316
C₈.₇C₂⁴ = D₈⋊C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	16	8+	C8.7C2^4	128,2317
C₈.₈C₂⁴ = C₄.C₂⁵	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₈	32	8-	C8.8C2^4	128,2318
C₈.₉C₂⁴ = C₂²×D₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.9C2^4	128,2140
C₈.₁₀C₂⁴ = C₂²×SD₃₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.10C2^4	128,2141
C₈.₁₁C₂⁴ = C₂²×Q₃₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	128		C8.11C2^4	128,2142
C₈.₁₂C₂⁴ = C₂×C₄○D₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.12C2^4	128,2143
C₈.₁₃C₂⁴ = C₂×C₁₆⋊C₂²	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	32		C8.13C2^4	128,2144
C₈.₁₄C₂⁴ = C₂×Q₃₂⋊C₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.14C2^4	128,2145
C₈.₁₅C₂⁴ = D₁₆⋊C₂²	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	32	4	C8.15C2^4	128,2146
C₈.₁₆C₂⁴ = D₄○D₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	32	4+	C8.16C2^4	128,2147
C₈.₁₇C₂⁴ = D₄○SD₃₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	32	4	C8.17C2^4	128,2148
C₈.₁₈C₂⁴ = Q₈○D₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64	4-	C8.18C2^4	128,2149
C₈.₁₉C₂⁴ = C₂³×Q₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	128		C8.19C2^4	128,2308
C₈.₂₀C₂⁴ = C₂²×C₄○D₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.20C2^4	128,2309
C₈.₂₁C₂⁴ = C₂²×C₈○D₄	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	64		C8.21C2^4	128,2303
C₈.₂₂C₂⁴ = C₂×Q₈○M₄(2)	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₈	32		C8.22C2^4	128,2304
C₈.₂₃C₂⁴ = C₂²×M₅(2)	central extension (φ=1)	64		C8.23C2^4	128,2137
C₈.₂₄C₂⁴ = C₂×D₄○C₁₆	central extension (φ=1)	64		C8.24C2^4	128,2138
C₈.₂₅C₂⁴ = Q₈○M₅(2)	central extension (φ=1)	32	4	C8.25C2^4	128,2139
C₈.₂₆C₂⁴ = C₄.₂₂C₂⁵	central extension (φ=1)	32	4	C8.26C2^4	128,2305

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Extensions 1→N→G→Q→1 with N=C8 and Q=C24

Extensions 1→N→G→Q→1 with N=C₈ and Q=C₂⁴