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

Direct product G=N×Q with N=C8 and Q=C24
dρLabelID
C24×C8128C2^4xC8128,2301

Semidirect products G=N:Q with N=C8 and Q=C24
extensionφ:Q→Aut NdρLabelID
C8⋊C24 = C22×C8⋊C22φ: C24/C22C22 ⊆ Aut C832C8:C2^4128,2310
C82C24 = C23×D8φ: C24/C23C2 ⊆ Aut C864C8:2C2^4128,2306
C83C24 = C23×SD16φ: C24/C23C2 ⊆ Aut C864C8:3C2^4128,2307
C84C24 = C23×M4(2)φ: C24/C23C2 ⊆ Aut C864C8:4C2^4128,2302

Non-split extensions G=N.Q with N=C8 and Q=C24
extensionφ:Q→Aut NdρLabelID
C8.1C24 = C22×C8.C22φ: C24/C22C22 ⊆ Aut C864C8.1C2^4128,2311
C8.2C24 = C2×D8⋊C22φ: C24/C22C22 ⊆ Aut C832C8.2C2^4128,2312
C8.3C24 = C2×D4○D8φ: C24/C22C22 ⊆ Aut C832C8.3C2^4128,2313
C8.4C24 = C2×D4○SD16φ: C24/C22C22 ⊆ Aut C832C8.4C2^4128,2314
C8.5C24 = C2×Q8○D8φ: C24/C22C22 ⊆ Aut C864C8.5C2^4128,2315
C8.6C24 = C8.C24φ: C24/C22C22 ⊆ Aut C8324C8.6C2^4128,2316
C8.7C24 = D8⋊C23φ: C24/C22C22 ⊆ Aut C8168+C8.7C2^4128,2317
C8.8C24 = C4.C25φ: C24/C22C22 ⊆ Aut C8328-C8.8C2^4128,2318
C8.9C24 = C22×D16φ: C24/C23C2 ⊆ Aut C864C8.9C2^4128,2140
C8.10C24 = C22×SD32φ: C24/C23C2 ⊆ Aut C864C8.10C2^4128,2141
C8.11C24 = C22×Q32φ: C24/C23C2 ⊆ Aut C8128C8.11C2^4128,2142
C8.12C24 = C2×C4○D16φ: C24/C23C2 ⊆ Aut C864C8.12C2^4128,2143
C8.13C24 = C2×C16⋊C22φ: C24/C23C2 ⊆ Aut C832C8.13C2^4128,2144
C8.14C24 = C2×Q32⋊C2φ: C24/C23C2 ⊆ Aut C864C8.14C2^4128,2145
C8.15C24 = D16⋊C22φ: C24/C23C2 ⊆ Aut C8324C8.15C2^4128,2146
C8.16C24 = D4○D16φ: C24/C23C2 ⊆ Aut C8324+C8.16C2^4128,2147
C8.17C24 = D4○SD32φ: C24/C23C2 ⊆ Aut C8324C8.17C2^4128,2148
C8.18C24 = Q8○D16φ: C24/C23C2 ⊆ Aut C8644-C8.18C2^4128,2149
C8.19C24 = C23×Q16φ: C24/C23C2 ⊆ Aut C8128C8.19C2^4128,2308
C8.20C24 = C22×C4○D8φ: C24/C23C2 ⊆ Aut C864C8.20C2^4128,2309
C8.21C24 = C22×C8○D4φ: C24/C23C2 ⊆ Aut C864C8.21C2^4128,2303
C8.22C24 = C2×Q8○M4(2)φ: C24/C23C2 ⊆ Aut C832C8.22C2^4128,2304
C8.23C24 = C22×M5(2)central extension (φ=1)64C8.23C2^4128,2137
C8.24C24 = C2×D4○C16central extension (φ=1)64C8.24C2^4128,2138
C8.25C24 = Q8○M5(2)central extension (φ=1)324C8.25C2^4128,2139
C8.26C24 = C4.22C25central extension (φ=1)324C8.26C2^4128,2305

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