# Extensions 1→N→G→Q→1 with N=D4 and Q=C24

Direct product G=N×Q with N=D4 and Q=C24
dρLabelID
D4×C2464D4xC2^4128,2320

Semidirect products G=N:Q with N=D4 and Q=C24
extensionφ:Q→Out NdρLabelID
D41C24 = C23×D8φ: C24/C23C2 ⊆ Out D464D4:1C2^4128,2306
D42C24 = C22×C8⋊C22φ: C24/C23C2 ⊆ Out D432D4:2C2^4128,2310
D43C24 = C23×C4○D4φ: trivial image64D4:3C2^4128,2322
D44C24 = C22×2+ 1+4φ: trivial image32D4:4C2^4128,2323

Non-split extensions G=N.Q with N=D4 and Q=C24
extensionφ:Q→Out NdρLabelID
D4.1C24 = C23×SD16φ: C24/C23C2 ⊆ Out D464D4.1C2^4128,2307
D4.2C24 = C22×C4○D8φ: C24/C23C2 ⊆ Out D464D4.2C2^4128,2309
D4.3C24 = C22×C8.C22φ: C24/C23C2 ⊆ Out D464D4.3C2^4128,2311
D4.4C24 = C2×D8⋊C22φ: C24/C23C2 ⊆ Out D432D4.4C2^4128,2312
D4.5C24 = C2×D4○D8φ: C24/C23C2 ⊆ Out D432D4.5C2^4128,2313
D4.6C24 = C2×D4○SD16φ: C24/C23C2 ⊆ Out D432D4.6C2^4128,2314
D4.7C24 = C2×Q8○D8φ: C24/C23C2 ⊆ Out D464D4.7C2^4128,2315
D4.8C24 = C8.C24φ: C24/C23C2 ⊆ Out D4324D4.8C2^4128,2316
D4.9C24 = D8⋊C23φ: C24/C23C2 ⊆ Out D4168+D4.9C2^4128,2317
D4.10C24 = C4.C25φ: C24/C23C2 ⊆ Out D4328-D4.10C2^4128,2318
D4.11C24 = C22×2- 1+4φ: trivial image64D4.11C2^4128,2324
D4.12C24 = C2×C2.C25φ: trivial image32D4.12C2^4128,2325
D4.13C24 = 2+ 1+6φ: trivial image168+D4.13C2^4128,2326
D4.14C24 = 2- 1+6φ: trivial image328-D4.14C2^4128,2327

׿
×
𝔽