# Extensions 1→N→G→Q→1 with N=C6 and Q=S3×C6

Direct product G=N×Q with N=C6 and Q=S3×C6
dρLabelID
S3×C6272S3xC6^2216,174

Semidirect products G=N:Q with N=C6 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C61(S3×C6) = S32×C6φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6:1(S3xC6)216,170
C62(S3×C6) = C2×C6×C3⋊S3φ: S3×C6/C3×C6C2 ⊆ Aut C672C6:2(S3xC6)216,175

Non-split extensions G=N.Q with N=C6 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C6.1(S3×C6) = C3×S3×Dic3φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6.1(S3xC6)216,119
C6.2(S3×C6) = C3×C6.D6φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6.2(S3xC6)216,120
C6.3(S3×C6) = C3×D6⋊S3φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6.3(S3xC6)216,121
C6.4(S3×C6) = C3×C3⋊D12φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6.4(S3xC6)216,122
C6.5(S3×C6) = C3×C322Q8φ: S3×C6/C3×S3C2 ⊆ Aut C6244C6.5(S3xC6)216,123
C6.6(S3×C6) = C3×Dic18φ: S3×C6/C3×C6C2 ⊆ Aut C6722C6.6(S3xC6)216,43
C6.7(S3×C6) = C12×D9φ: S3×C6/C3×C6C2 ⊆ Aut C6722C6.7(S3xC6)216,45
C6.8(S3×C6) = C3×D36φ: S3×C6/C3×C6C2 ⊆ Aut C6722C6.8(S3xC6)216,46
C6.9(S3×C6) = He33Q8φ: S3×C6/C3×C6C2 ⊆ Aut C6726-C6.9(S3xC6)216,49
C6.10(S3×C6) = C4×C32⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C6366C6.10(S3xC6)216,50
C6.11(S3×C6) = He34D4φ: S3×C6/C3×C6C2 ⊆ Aut C6366+C6.11(S3xC6)216,51
C6.12(S3×C6) = C36.C6φ: S3×C6/C3×C6C2 ⊆ Aut C6726-C6.12(S3xC6)216,52
C6.13(S3×C6) = C4×C9⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C6366C6.13(S3xC6)216,53
C6.14(S3×C6) = D36⋊C3φ: S3×C6/C3×C6C2 ⊆ Aut C6366+C6.14(S3xC6)216,54
C6.15(S3×C6) = C6×Dic9φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.15(S3xC6)216,55
C6.16(S3×C6) = C3×C9⋊D4φ: S3×C6/C3×C6C2 ⊆ Aut C6362C6.16(S3xC6)216,57
C6.17(S3×C6) = C2×C32⋊C12φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.17(S3xC6)216,59
C6.18(S3×C6) = He36D4φ: S3×C6/C3×C6C2 ⊆ Aut C6366C6.18(S3xC6)216,60
C6.19(S3×C6) = C2×C9⋊C12φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.19(S3xC6)216,61
C6.20(S3×C6) = Dic9⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C6366C6.20(S3xC6)216,62
C6.21(S3×C6) = C2×C6×D9φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.21(S3xC6)216,108
C6.22(S3×C6) = C22×C32⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C636C6.22(S3xC6)216,110
C6.23(S3×C6) = C22×C9⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C636C6.23(S3xC6)216,111
C6.24(S3×C6) = C3×C324Q8φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.24(S3xC6)216,140
C6.25(S3×C6) = C12×C3⋊S3φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.25(S3xC6)216,141
C6.26(S3×C6) = C3×C12⋊S3φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.26(S3xC6)216,142
C6.27(S3×C6) = C6×C3⋊Dic3φ: S3×C6/C3×C6C2 ⊆ Aut C672C6.27(S3xC6)216,143
C6.28(S3×C6) = C3×C327D4φ: S3×C6/C3×C6C2 ⊆ Aut C636C6.28(S3xC6)216,144
C6.29(S3×C6) = C9×Dic6central extension (φ=1)722C6.29(S3xC6)216,44
C6.30(S3×C6) = S3×C36central extension (φ=1)722C6.30(S3xC6)216,47
C6.31(S3×C6) = C9×D12central extension (φ=1)722C6.31(S3xC6)216,48
C6.32(S3×C6) = Dic3×C18central extension (φ=1)72C6.32(S3xC6)216,56
C6.33(S3×C6) = C9×C3⋊D4central extension (φ=1)362C6.33(S3xC6)216,58
C6.34(S3×C6) = S3×C2×C18central extension (φ=1)72C6.34(S3xC6)216,109
C6.35(S3×C6) = C32×Dic6central extension (φ=1)72C6.35(S3xC6)216,135
C6.36(S3×C6) = S3×C3×C12central extension (φ=1)72C6.36(S3xC6)216,136
C6.37(S3×C6) = C32×D12central extension (φ=1)72C6.37(S3xC6)216,137
C6.38(S3×C6) = Dic3×C3×C6central extension (φ=1)72C6.38(S3xC6)216,138
C6.39(S3×C6) = C32×C3⋊D4central extension (φ=1)36C6.39(S3xC6)216,139

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