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

Direct product G=N×Q with N=Q8 and Q=C24
dρLabelID
Q8×C24128Q8xC2^4128,2321

Semidirect products G=N:Q with N=Q8 and Q=C24
extensionφ:Q→Out NdρLabelID
Q81C24 = C23×SD16φ: C24/C23C2 ⊆ Out Q864Q8:1C2^4128,2307
Q82C24 = C22×C8⋊C22φ: C24/C23C2 ⊆ Out Q832Q8:2C2^4128,2310
Q83C24 = C23×C4○D4φ: trivial image64Q8:3C2^4128,2322
Q84C24 = C22×2+ 1+4φ: trivial image32Q8:4C2^4128,2323

Non-split extensions G=N.Q with N=Q8 and Q=C24
extensionφ:Q→Out NdρLabelID
Q8.1C24 = C23×Q16φ: C24/C23C2 ⊆ Out Q8128Q8.1C2^4128,2308
Q8.2C24 = C22×C4○D8φ: C24/C23C2 ⊆ Out Q864Q8.2C2^4128,2309
Q8.3C24 = C22×C8.C22φ: C24/C23C2 ⊆ Out Q864Q8.3C2^4128,2311
Q8.4C24 = C2×D8⋊C22φ: C24/C23C2 ⊆ Out Q832Q8.4C2^4128,2312
Q8.5C24 = C2×D4○D8φ: C24/C23C2 ⊆ Out Q832Q8.5C2^4128,2313
Q8.6C24 = C2×D4○SD16φ: C24/C23C2 ⊆ Out Q832Q8.6C2^4128,2314
Q8.7C24 = C2×Q8○D8φ: C24/C23C2 ⊆ Out Q864Q8.7C2^4128,2315
Q8.8C24 = C8.C24φ: C24/C23C2 ⊆ Out Q8324Q8.8C2^4128,2316
Q8.9C24 = D8⋊C23φ: C24/C23C2 ⊆ Out Q8168+Q8.9C2^4128,2317
Q8.10C24 = C4.C25φ: C24/C23C2 ⊆ Out Q8328-Q8.10C2^4128,2318
Q8.11C24 = C22×2- 1+4φ: trivial image64Q8.11C2^4128,2324
Q8.12C24 = C2×C2.C25φ: trivial image32Q8.12C2^4128,2325
Q8.13C24 = 2+ 1+6φ: trivial image168+Q8.13C2^4128,2326
Q8.14C24 = 2- 1+6φ: trivial image328-Q8.14C2^4128,2327

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