# Extensions 1→N→G→Q→1 with N=C12 and Q=S32

Direct product G=N×Q with N=C12 and Q=S32
dρLabelID
S32×C12484S3^2xC12432,648

Semidirect products G=N:Q with N=C12 and Q=S32
extensionφ:Q→Aut NdρLabelID
C121S32 = C3⋊S3×D12φ: S32/C32C22 ⊆ Aut C1272C12:1S3^2432,672
C122S32 = C12⋊S32φ: S32/C32C22 ⊆ Aut C1272C12:2S3^2432,673
C123S32 = C123S32φ: S32/C32C22 ⊆ Aut C12484C12:3S3^2432,691
C124S32 = S3×C12⋊S3φ: S32/C3×S3C2 ⊆ Aut C1272C12:4S3^2432,671
C125S32 = C4×S3×C3⋊S3φ: S32/C3×S3C2 ⊆ Aut C1272C12:5S3^2432,670
C126S32 = C3×S3×D12φ: S32/C3×S3C2 ⊆ Aut C12484C12:6S3^2432,649
C127S32 = C4×C324D6φ: S32/C3⋊S3C2 ⊆ Aut C12484C12:7S3^2432,690
C128S32 = C3×D6⋊D6φ: S32/C3⋊S3C2 ⊆ Aut C12484C12:8S3^2432,650

Non-split extensions G=N.Q with N=C12 and Q=S32
extensionφ:Q→Aut NdρLabelID
C12.1S32 = D36⋊S3φ: S32/C32C22 ⊆ Aut C121444C12.1S3^2432,68
C12.2S32 = C9⋊D24φ: S32/C32C22 ⊆ Aut C12724+C12.2S3^2432,69
C12.3S32 = D12.D9φ: S32/C32C22 ⊆ Aut C121444C12.3S3^2432,70
C12.4S32 = C36.D6φ: S32/C32C22 ⊆ Aut C121444-C12.4S3^2432,71
C12.5S32 = Dic6⋊D9φ: S32/C32C22 ⊆ Aut C121444C12.5S3^2432,72
C12.6S32 = C18.D12φ: S32/C32C22 ⊆ Aut C12724+C12.6S3^2432,73
C12.7S32 = C12.D18φ: S32/C32C22 ⊆ Aut C121444C12.7S3^2432,74
C12.8S32 = C9⋊Dic12φ: S32/C32C22 ⊆ Aut C121444-C12.8S3^2432,75
C12.9S32 = He33D8φ: S32/C32C22 ⊆ Aut C127212+C12.9S3^2432,83
C12.10S32 = He34SD16φ: S32/C32C22 ⊆ Aut C127212-C12.10S3^2432,84
C12.11S32 = He35SD16φ: S32/C32C22 ⊆ Aut C127212+C12.11S3^2432,85
C12.12S32 = He33Q16φ: S32/C32C22 ⊆ Aut C1214412-C12.12S3^2432,86
C12.13S32 = D9×Dic6φ: S32/C32C22 ⊆ Aut C121444-C12.13S3^2432,280
C12.14S32 = D18.D6φ: S32/C32C22 ⊆ Aut C12724C12.14S3^2432,281
C12.15S32 = Dic65D9φ: S32/C32C22 ⊆ Aut C12724+C12.15S3^2432,282
C12.16S32 = Dic18⋊S3φ: S32/C32C22 ⊆ Aut C12724C12.16S3^2432,283
C12.17S32 = D125D9φ: S32/C32C22 ⊆ Aut C121444-C12.17S3^2432,285
C12.18S32 = D12⋊D9φ: S32/C32C22 ⊆ Aut C12724C12.18S3^2432,286
C12.19S32 = D9×D12φ: S32/C32C22 ⊆ Aut C12724+C12.19S3^2432,292
C12.20S32 = C36⋊D6φ: S32/C32C22 ⊆ Aut C12724C12.20S3^2432,293
C12.21S32 = C3⋊S3⋊Dic6φ: S32/C32C22 ⊆ Aut C127212-C12.21S3^2432,294
C12.22S32 = C12⋊S3⋊S3φ: S32/C32C22 ⊆ Aut C127212+C12.22S3^2432,295
C12.23S32 = C12.S32φ: S32/C32C22 ⊆ Aut C127212-C12.23S3^2432,299
C12.24S32 = C3⋊S3⋊D12φ: S32/C32C22 ⊆ Aut C123612+C12.24S3^2432,301
C12.25S32 = C336D8φ: S32/C32C22 ⊆ Aut C12144C12.25S3^2432,436
C12.26S32 = C337D8φ: S32/C32C22 ⊆ Aut C1272C12.26S3^2432,437
C12.27S32 = C3312SD16φ: S32/C32C22 ⊆ Aut C12144C12.27S3^2432,439
C12.28S32 = C3313SD16φ: S32/C32C22 ⊆ Aut C12144C12.28S3^2432,440
C12.29S32 = C3314SD16φ: S32/C32C22 ⊆ Aut C12144C12.29S3^2432,441
C12.30S32 = C3315SD16φ: S32/C32C22 ⊆ Aut C1272C12.30S3^2432,442
C12.31S32 = C336Q16φ: S32/C32C22 ⊆ Aut C12144C12.31S3^2432,445
C12.32S32 = C337Q16φ: S32/C32C22 ⊆ Aut C12144C12.32S3^2432,446
C12.33S32 = C339D8φ: S32/C32C22 ⊆ Aut C12484C12.33S3^2432,457
C12.34S32 = C3318SD16φ: S32/C32C22 ⊆ Aut C12484C12.34S3^2432,458
C12.35S32 = C339Q16φ: S32/C32C22 ⊆ Aut C12484C12.35S3^2432,459
C12.36S32 = (C3×D12)⋊S3φ: S32/C32C22 ⊆ Aut C12144C12.36S3^2432,661
C12.37S32 = D12⋊(C3⋊S3)φ: S32/C32C22 ⊆ Aut C1272C12.37S3^2432,662
C12.38S32 = C3⋊S3×Dic6φ: S32/C32C22 ⊆ Aut C12144C12.38S3^2432,663
C12.39S32 = C12.39S32φ: S32/C32C22 ⊆ Aut C1272C12.39S3^2432,664
C12.40S32 = C12.40S32φ: S32/C32C22 ⊆ Aut C1272C12.40S3^2432,665
C12.41S32 = C329(S3×Q8)φ: S32/C32C22 ⊆ Aut C1272C12.41S3^2432,666
C12.42S32 = C3⋊S34Dic6φ: S32/C32C22 ⊆ Aut C12484C12.42S3^2432,687
C12.43S32 = C12⋊S312S3φ: S32/C32C22 ⊆ Aut C12484C12.43S3^2432,688
C12.44S32 = D36.S3φ: S32/C3×S3C2 ⊆ Aut C121444-C12.44S3^2432,62
C12.45S32 = C6.D36φ: S32/C3×S3C2 ⊆ Aut C12724+C12.45S3^2432,63
C12.46S32 = C3⋊D72φ: S32/C3×S3C2 ⊆ Aut C12724+C12.46S3^2432,64
C12.47S32 = C3⋊Dic36φ: S32/C3×S3C2 ⊆ Aut C121444-C12.47S3^2432,65
C12.48S32 = S3×Dic18φ: S32/C3×S3C2 ⊆ Aut C121444-C12.48S3^2432,284
C12.49S32 = D365S3φ: S32/C3×S3C2 ⊆ Aut C121444-C12.49S3^2432,288
C12.50S32 = Dic9.D6φ: S32/C3×S3C2 ⊆ Aut C12724+C12.50S3^2432,289
C12.51S32 = S3×D36φ: S32/C3×S3C2 ⊆ Aut C12724+C12.51S3^2432,291
C12.52S32 = C338D8φ: S32/C3×S3C2 ⊆ Aut C1272C12.52S3^2432,438
C12.53S32 = C3316SD16φ: S32/C3×S3C2 ⊆ Aut C12144C12.53S3^2432,443
C12.54S32 = C3317SD16φ: S32/C3×S3C2 ⊆ Aut C1272C12.54S3^2432,444
C12.55S32 = C338Q16φ: S32/C3×S3C2 ⊆ Aut C12144C12.55S3^2432,447
C12.56S32 = S3×C324Q8φ: S32/C3×S3C2 ⊆ Aut C12144C12.56S3^2432,660
C12.57S32 = C12.57S32φ: S32/C3×S3C2 ⊆ Aut C12144C12.57S3^2432,668
C12.58S32 = C12.58S32φ: S32/C3×S3C2 ⊆ Aut C1272C12.58S3^2432,669
C12.59S32 = D9×C3⋊C8φ: S32/C3×S3C2 ⊆ Aut C121444C12.59S3^2432,58
C12.60S32 = C36.38D6φ: S32/C3×S3C2 ⊆ Aut C12724C12.60S3^2432,59
C12.61S32 = C36.39D6φ: S32/C3×S3C2 ⊆ Aut C121444C12.61S3^2432,60
C12.62S32 = C36.40D6φ: S32/C3×S3C2 ⊆ Aut C12724C12.62S3^2432,61
C12.63S32 = S3×C9⋊C8φ: S32/C3×S3C2 ⊆ Aut C121444C12.63S3^2432,66
C12.64S32 = D6.Dic9φ: S32/C3×S3C2 ⊆ Aut C121444C12.64S3^2432,67
C12.65S32 = D6.D18φ: S32/C3×S3C2 ⊆ Aut C12724C12.65S3^2432,287
C12.66S32 = C4×S3×D9φ: S32/C3×S3C2 ⊆ Aut C12724C12.66S3^2432,290
C12.67S32 = S3×C324C8φ: S32/C3×S3C2 ⊆ Aut C12144C12.67S3^2432,430
C12.68S32 = C3⋊S3×C3⋊C8φ: S32/C3×S3C2 ⊆ Aut C12144C12.68S3^2432,431
C12.69S32 = C12.69S32φ: S32/C3×S3C2 ⊆ Aut C1272C12.69S3^2432,432
C12.70S32 = C337M4(2)φ: S32/C3×S3C2 ⊆ Aut C12144C12.70S3^2432,433
C12.71S32 = C338M4(2)φ: S32/C3×S3C2 ⊆ Aut C12144C12.71S3^2432,434
C12.72S32 = C339M4(2)φ: S32/C3×S3C2 ⊆ Aut C1272C12.72S3^2432,435
C12.73S32 = C12.73S32φ: S32/C3×S3C2 ⊆ Aut C1272C12.73S3^2432,667
C12.74S32 = C3×C3⋊D24φ: S32/C3×S3C2 ⊆ Aut C12484C12.74S3^2432,419
C12.75S32 = C3×D12.S3φ: S32/C3×S3C2 ⊆ Aut C12484C12.75S3^2432,421
C12.76S32 = C3×C325SD16φ: S32/C3×S3C2 ⊆ Aut C12484C12.76S3^2432,422
C12.77S32 = C3×C323Q16φ: S32/C3×S3C2 ⊆ Aut C12484C12.77S3^2432,424
C12.78S32 = C3×S3×Dic6φ: S32/C3×S3C2 ⊆ Aut C12484C12.78S3^2432,642
C12.79S32 = C3×D125S3φ: S32/C3×S3C2 ⊆ Aut C12484C12.79S3^2432,643
C12.80S32 = C3×D6.6D6φ: S32/C3×S3C2 ⊆ Aut C12484C12.80S3^2432,647
C12.81S32 = He33SD16φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.81S3^2432,78
C12.82S32 = He32D8φ: S32/C3⋊S3C2 ⊆ Aut C12726+C12.82S3^2432,79
C12.83S32 = He32Q16φ: S32/C3⋊S3C2 ⊆ Aut C121446-C12.83S3^2432,80
C12.84S32 = C12.84S32φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.84S3^2432,296
C12.85S32 = C12.85S32φ: S32/C3⋊S3C2 ⊆ Aut C12726-C12.85S3^2432,298
C12.86S32 = C12.86S32φ: S32/C3⋊S3C2 ⊆ Aut C12366+C12.86S3^2432,302
C12.87S32 = C32⋊C6⋊C8φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.87S3^2432,76
C12.88S32 = He3⋊M4(2)φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.88S3^2432,77
C12.89S32 = C12.89S32φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.89S3^2432,81
C12.90S32 = He33M4(2)φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.90S3^2432,82
C12.91S32 = C12.91S32φ: S32/C3⋊S3C2 ⊆ Aut C12726C12.91S3^2432,297
C12.92S32 = C4×C32⋊D6φ: S32/C3⋊S3C2 ⊆ Aut C12366C12.92S3^2432,300
C12.93S32 = C12.93S32φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.93S3^2432,455
C12.94S32 = C3310M4(2)φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.94S3^2432,456
C12.95S32 = C12.95S32φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.95S3^2432,689
C12.96S32 = C3×C322D8φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.96S3^2432,418
C12.97S32 = C3×Dic6⋊S3φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.97S3^2432,420
C12.98S32 = C3×C322Q16φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.98S3^2432,423
C12.99S32 = C3×D12⋊S3φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.99S3^2432,644
C12.100S32 = C3×Dic3.D6φ: S32/C3⋊S3C2 ⊆ Aut C12484C12.100S3^2432,645
C12.101S32 = C3×S3×C3⋊C8central extension (φ=1)484C12.101S3^2432,414
C12.102S32 = C3×C12.29D6central extension (φ=1)484C12.102S3^2432,415
C12.103S32 = C3×D6.Dic3central extension (φ=1)484C12.103S3^2432,416
C12.104S32 = C3×C12.31D6central extension (φ=1)484C12.104S3^2432,417
C12.105S32 = C3×D6.D6central extension (φ=1)484C12.105S3^2432,646

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