# Extensions 1→N→G→Q→1 with N=C12 and Q=D6

Direct product G=N×Q with N=C12 and Q=D6
dρLabelID
S3×C2×C1248S3xC2xC12144,159

Semidirect products G=N:Q with N=C12 and Q=D6
extensionφ:Q→Aut NdρLabelID
C121D6 = S3×D12φ: D6/C3C22 ⊆ Aut C12244+C12:1D6144,144
C122D6 = D6⋊D6φ: D6/C3C22 ⊆ Aut C12244C12:2D6144,145
C123D6 = D4×C3⋊S3φ: D6/C3C22 ⊆ Aut C1236C12:3D6144,172
C124D6 = C4×S32φ: D6/S3C2 ⊆ Aut C12244C12:4D6144,143
C125D6 = C3×S3×D4φ: D6/S3C2 ⊆ Aut C12244C12:5D6144,162
C126D6 = C2×C12⋊S3φ: D6/C6C2 ⊆ Aut C1272C12:6D6144,170
C127D6 = C2×C4×C3⋊S3φ: D6/C6C2 ⊆ Aut C1272C12:7D6144,169
C128D6 = C6×D12φ: D6/C6C2 ⊆ Aut C1248C12:8D6144,160

Non-split extensions G=N.Q with N=C12 and Q=D6
extensionφ:Q→Aut NdρLabelID
C12.1D6 = D4.D9φ: D6/C3C22 ⊆ Aut C12724-C12.1D6144,15
C12.2D6 = D4⋊D9φ: D6/C3C22 ⊆ Aut C12724+C12.2D6144,16
C12.3D6 = C9⋊Q16φ: D6/C3C22 ⊆ Aut C121444-C12.3D6144,17
C12.4D6 = Q82D9φ: D6/C3C22 ⊆ Aut C12724+C12.4D6144,18
C12.5D6 = D4×D9φ: D6/C3C22 ⊆ Aut C12364+C12.5D6144,41
C12.6D6 = D42D9φ: D6/C3C22 ⊆ Aut C12724-C12.6D6144,42
C12.7D6 = Q8×D9φ: D6/C3C22 ⊆ Aut C12724-C12.7D6144,43
C12.8D6 = Q83D9φ: D6/C3C22 ⊆ Aut C12724+C12.8D6144,44
C12.9D6 = C322D8φ: D6/C3C22 ⊆ Aut C12484C12.9D6144,56
C12.10D6 = C3⋊D24φ: D6/C3C22 ⊆ Aut C12244+C12.10D6144,57
C12.11D6 = Dic6⋊S3φ: D6/C3C22 ⊆ Aut C12484C12.11D6144,58
C12.12D6 = D12.S3φ: D6/C3C22 ⊆ Aut C12484-C12.12D6144,59
C12.13D6 = C325SD16φ: D6/C3C22 ⊆ Aut C12244+C12.13D6144,60
C12.14D6 = C322Q16φ: D6/C3C22 ⊆ Aut C12484C12.14D6144,61
C12.15D6 = C323Q16φ: D6/C3C22 ⊆ Aut C12484-C12.15D6144,62
C12.16D6 = C327D8φ: D6/C3C22 ⊆ Aut C1272C12.16D6144,96
C12.17D6 = C329SD16φ: D6/C3C22 ⊆ Aut C1272C12.17D6144,97
C12.18D6 = C3211SD16φ: D6/C3C22 ⊆ Aut C1272C12.18D6144,98
C12.19D6 = C327Q16φ: D6/C3C22 ⊆ Aut C12144C12.19D6144,99
C12.20D6 = S3×Dic6φ: D6/C3C22 ⊆ Aut C12484-C12.20D6144,137
C12.21D6 = D125S3φ: D6/C3C22 ⊆ Aut C12484-C12.21D6144,138
C12.22D6 = D12⋊S3φ: D6/C3C22 ⊆ Aut C12244C12.22D6144,139
C12.23D6 = Dic3.D6φ: D6/C3C22 ⊆ Aut C12244C12.23D6144,140
C12.24D6 = C12.D6φ: D6/C3C22 ⊆ Aut C1272C12.24D6144,173
C12.25D6 = Q8×C3⋊S3φ: D6/C3C22 ⊆ Aut C1272C12.25D6144,174
C12.26D6 = C12.26D6φ: D6/C3C22 ⊆ Aut C1272C12.26D6144,175
C12.27D6 = D6.6D6φ: D6/S3C2 ⊆ Aut C12244+C12.27D6144,142
C12.28D6 = S3×C3⋊C8φ: D6/S3C2 ⊆ Aut C12484C12.28D6144,52
C12.29D6 = C12.29D6φ: D6/S3C2 ⊆ Aut C12244C12.29D6144,53
C12.30D6 = D6.Dic3φ: D6/S3C2 ⊆ Aut C12484C12.30D6144,54
C12.31D6 = C12.31D6φ: D6/S3C2 ⊆ Aut C12244C12.31D6144,55
C12.32D6 = D6.D6φ: D6/S3C2 ⊆ Aut C12244C12.32D6144,141
C12.33D6 = C3×D4⋊S3φ: D6/S3C2 ⊆ Aut C12244C12.33D6144,80
C12.34D6 = C3×D4.S3φ: D6/S3C2 ⊆ Aut C12244C12.34D6144,81
C12.35D6 = C3×Q82S3φ: D6/S3C2 ⊆ Aut C12484C12.35D6144,82
C12.36D6 = C3×C3⋊Q16φ: D6/S3C2 ⊆ Aut C12484C12.36D6144,83
C12.37D6 = C3×D42S3φ: D6/S3C2 ⊆ Aut C12244C12.37D6144,163
C12.38D6 = C3×S3×Q8φ: D6/S3C2 ⊆ Aut C12484C12.38D6144,164
C12.39D6 = C3×Q83S3φ: D6/S3C2 ⊆ Aut C12484C12.39D6144,165
C12.40D6 = Dic36φ: D6/C6C2 ⊆ Aut C121442-C12.40D6144,4
C12.41D6 = C72⋊C2φ: D6/C6C2 ⊆ Aut C12722C12.41D6144,7
C12.42D6 = D72φ: D6/C6C2 ⊆ Aut C12722+C12.42D6144,8
C12.43D6 = C2×Dic18φ: D6/C6C2 ⊆ Aut C12144C12.43D6144,37
C12.44D6 = C2×D36φ: D6/C6C2 ⊆ Aut C1272C12.44D6144,39
C12.45D6 = D365C2φ: D6/C6C2 ⊆ Aut C12722C12.45D6144,40
C12.46D6 = C242S3φ: D6/C6C2 ⊆ Aut C1272C12.46D6144,87
C12.47D6 = C325D8φ: D6/C6C2 ⊆ Aut C1272C12.47D6144,88
C12.48D6 = C325Q16φ: D6/C6C2 ⊆ Aut C12144C12.48D6144,89
C12.49D6 = C2×C324Q8φ: D6/C6C2 ⊆ Aut C12144C12.49D6144,168
C12.50D6 = C8×D9φ: D6/C6C2 ⊆ Aut C12722C12.50D6144,5
C12.51D6 = C8⋊D9φ: D6/C6C2 ⊆ Aut C12722C12.51D6144,6
C12.52D6 = C2×C9⋊C8φ: D6/C6C2 ⊆ Aut C12144C12.52D6144,9
C12.53D6 = C4.Dic9φ: D6/C6C2 ⊆ Aut C12722C12.53D6144,10
C12.54D6 = C2×C4×D9φ: D6/C6C2 ⊆ Aut C1272C12.54D6144,38
C12.55D6 = C8×C3⋊S3φ: D6/C6C2 ⊆ Aut C1272C12.55D6144,85
C12.56D6 = C24⋊S3φ: D6/C6C2 ⊆ Aut C1272C12.56D6144,86
C12.57D6 = C2×C324C8φ: D6/C6C2 ⊆ Aut C12144C12.57D6144,90
C12.58D6 = C12.58D6φ: D6/C6C2 ⊆ Aut C1272C12.58D6144,91
C12.59D6 = C12.59D6φ: D6/C6C2 ⊆ Aut C1272C12.59D6144,171
C12.60D6 = C3×C24⋊C2φ: D6/C6C2 ⊆ Aut C12482C12.60D6144,71
C12.61D6 = C3×D24φ: D6/C6C2 ⊆ Aut C12482C12.61D6144,72
C12.62D6 = C3×Dic12φ: D6/C6C2 ⊆ Aut C12482C12.62D6144,73
C12.63D6 = C6×Dic6φ: D6/C6C2 ⊆ Aut C1248C12.63D6144,158
C12.64D6 = S3×C24central extension (φ=1)482C12.64D6144,69
C12.65D6 = C3×C8⋊S3central extension (φ=1)482C12.65D6144,70
C12.66D6 = C6×C3⋊C8central extension (φ=1)48C12.66D6144,74
C12.67D6 = C3×C4.Dic3central extension (φ=1)242C12.67D6144,75
C12.68D6 = C3×C4○D12central extension (φ=1)242C12.68D6144,161

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