# Extensions 1→N→G→Q→1 with N=C12 and Q=C62

Direct product G=N×Q with N=C12 and Q=C62
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C12 and Q=C62
extensionφ:Q→Aut NdρLabelID
C12⋊C62 = S3×D4×C32φ: C62/C32C22 ⊆ Aut C1272C12:C6^2432,704
C122C62 = C3×C6×D12φ: C62/C3×C6C2 ⊆ Aut C12144C12:2C6^2432,702
C123C62 = S3×C6×C12φ: C62/C3×C6C2 ⊆ Aut C12144C12:3C6^2432,701
C124C62 = D4×C32×C6φ: C62/C3×C6C2 ⊆ Aut C12216C12:4C6^2432,731

Non-split extensions G=N.Q with N=C12 and Q=C62
extensionφ:Q→Aut NdρLabelID
C12.1C62 = C32×D4⋊S3φ: C62/C32C22 ⊆ Aut C1272C12.1C6^2432,475
C12.2C62 = C32×D4.S3φ: C62/C32C22 ⊆ Aut C1272C12.2C6^2432,476
C12.3C62 = C32×Q82S3φ: C62/C32C22 ⊆ Aut C12144C12.3C6^2432,477
C12.4C62 = C32×C3⋊Q16φ: C62/C32C22 ⊆ Aut C12144C12.4C6^2432,478
C12.5C62 = C32×D42S3φ: C62/C32C22 ⊆ Aut C1272C12.5C6^2432,705
C12.6C62 = S3×Q8×C32φ: C62/C32C22 ⊆ Aut C12144C12.6C6^2432,706
C12.7C62 = C32×Q83S3φ: C62/C32C22 ⊆ Aut C12144C12.7C6^2432,707
C12.8C62 = C32×C24⋊C2φ: C62/C3×C6C2 ⊆ Aut C12144C12.8C6^2432,466
C12.9C62 = C32×D24φ: C62/C3×C6C2 ⊆ Aut C12144C12.9C6^2432,467
C12.10C62 = C32×Dic12φ: C62/C3×C6C2 ⊆ Aut C12144C12.10C6^2432,468
C12.11C62 = C3×C6×Dic6φ: C62/C3×C6C2 ⊆ Aut C12144C12.11C6^2432,700
C12.12C62 = S3×C3×C24φ: C62/C3×C6C2 ⊆ Aut C12144C12.12C6^2432,464
C12.13C62 = C32×C8⋊S3φ: C62/C3×C6C2 ⊆ Aut C12144C12.13C6^2432,465
C12.14C62 = C3×C6×C3⋊C8φ: C62/C3×C6C2 ⊆ Aut C12144C12.14C6^2432,469
C12.15C62 = C32×C4.Dic3φ: C62/C3×C6C2 ⊆ Aut C1272C12.15C6^2432,470
C12.16C62 = C32×C4○D12φ: C62/C3×C6C2 ⊆ Aut C1272C12.16C6^2432,703
C12.17C62 = D8×C3×C9φ: C62/C3×C6C2 ⊆ Aut C12216C12.17C6^2432,215
C12.18C62 = D8×He3φ: C62/C3×C6C2 ⊆ Aut C12726C12.18C6^2432,216
C12.19C62 = D8×3- 1+2φ: C62/C3×C6C2 ⊆ Aut C12726C12.19C6^2432,217
C12.20C62 = SD16×C3×C9φ: C62/C3×C6C2 ⊆ Aut C12216C12.20C6^2432,218
C12.21C62 = SD16×He3φ: C62/C3×C6C2 ⊆ Aut C12726C12.21C6^2432,219
C12.22C62 = SD16×3- 1+2φ: C62/C3×C6C2 ⊆ Aut C12726C12.22C6^2432,220
C12.23C62 = Q16×C3×C9φ: C62/C3×C6C2 ⊆ Aut C12432C12.23C6^2432,221
C12.24C62 = Q16×He3φ: C62/C3×C6C2 ⊆ Aut C121446C12.24C6^2432,222
C12.25C62 = Q16×3- 1+2φ: C62/C3×C6C2 ⊆ Aut C121446C12.25C6^2432,223
C12.26C62 = D4×C3×C18φ: C62/C3×C6C2 ⊆ Aut C12216C12.26C6^2432,403
C12.27C62 = C2×D4×He3φ: C62/C3×C6C2 ⊆ Aut C1272C12.27C6^2432,404
C12.28C62 = C2×D4×3- 1+2φ: C62/C3×C6C2 ⊆ Aut C1272C12.28C6^2432,405
C12.29C62 = Q8×C3×C18φ: C62/C3×C6C2 ⊆ Aut C12432C12.29C6^2432,406
C12.30C62 = C2×Q8×He3φ: C62/C3×C6C2 ⊆ Aut C12144C12.30C6^2432,407
C12.31C62 = C2×Q8×3- 1+2φ: C62/C3×C6C2 ⊆ Aut C12144C12.31C6^2432,408
C12.32C62 = C4○D4×C3×C9φ: C62/C3×C6C2 ⊆ Aut C12216C12.32C6^2432,409
C12.33C62 = D8×C33φ: C62/C3×C6C2 ⊆ Aut C12216C12.33C6^2432,517
C12.34C62 = SD16×C33φ: C62/C3×C6C2 ⊆ Aut C12216C12.34C6^2432,518
C12.35C62 = Q16×C33φ: C62/C3×C6C2 ⊆ Aut C12432C12.35C6^2432,519
C12.36C62 = Q8×C32×C6φ: C62/C3×C6C2 ⊆ Aut C12432C12.36C6^2432,732
C12.37C62 = C4○D4×C33φ: C62/C3×C6C2 ⊆ Aut C12216C12.37C6^2432,733
C12.38C62 = C2×C8×He3central extension (φ=1)144C12.38C6^2432,210
C12.39C62 = C2×C8×3- 1+2central extension (φ=1)144C12.39C6^2432,211
C12.40C62 = M4(2)×C3×C9central extension (φ=1)216C12.40C6^2432,212
C12.41C62 = M4(2)×He3central extension (φ=1)726C12.41C6^2432,213
C12.42C62 = M4(2)×3- 1+2central extension (φ=1)726C12.42C6^2432,214
C12.43C62 = C22×C4×He3central extension (φ=1)144C12.43C6^2432,401
C12.44C62 = C22×C4×3- 1+2central extension (φ=1)144C12.44C6^2432,402
C12.45C62 = C4○D4×He3central extension (φ=1)726C12.45C6^2432,410
C12.46C62 = C4○D4×3- 1+2central extension (φ=1)726C12.46C6^2432,411
C12.47C62 = M4(2)×C33central extension (φ=1)216C12.47C6^2432,516

׿
×
𝔽