# Extensions 1→N→G→Q→1 with N=C32 and Q=S3×C6

Direct product G=N×Q with N=C32 and Q=S3×C6
dρLabelID
S3×C32×C6108S3xC3^2xC6324,172

Semidirect products G=N:Q with N=C32 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C32⋊(S3×C6) = C3×C32⋊D6φ: S3×C6/C3D6 ⊆ Aut C32186C3^2:(S3xC6)324,117
C322(S3×C6) = S3×C32⋊C6φ: S3×C6/S3C6 ⊆ Aut C321812+C3^2:2(S3xC6)324,116
C323(S3×C6) = C6×C32⋊C6φ: S3×C6/C6S3 ⊆ Aut C32366C3^2:3(S3xC6)324,138
C324(S3×C6) = C6×He3⋊C2φ: S3×C6/C6S3 ⊆ Aut C3254C3^2:4(S3xC6)324,145
C325(S3×C6) = C2×He34S3φ: S3×C6/C6C6 ⊆ Aut C3254C3^2:5(S3xC6)324,144
C326(S3×C6) = C3×S3×C3⋊S3φ: S3×C6/C32C22 ⊆ Aut C3236C3^2:6(S3xC6)324,166
C327(S3×C6) = C3×C324D6φ: S3×C6/C32C22 ⊆ Aut C32124C3^2:7(S3xC6)324,167
C328(S3×C6) = C2×S3×He3φ: S3×C6/D6C3 ⊆ Aut C32366C3^2:8(S3xC6)324,139
C329(S3×C6) = S32×C32φ: S3×C6/C3×S3C2 ⊆ Aut C3236C3^2:9(S3xC6)324,165
C3210(S3×C6) = C3⋊S3×C3×C6φ: S3×C6/C3×C6C2 ⊆ Aut C3236C3^2:10(S3xC6)324,173
C3211(S3×C6) = C6×C33⋊C2φ: S3×C6/C3×C6C2 ⊆ Aut C32108C3^2:11(S3xC6)324,174

Non-split extensions G=N.Q with N=C32 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C32.1(S3×C6) = C2×C3≀S3φ: S3×C6/C6S3 ⊆ Aut C32183C3^2.1(S3xC6)324,68
C32.2(S3×C6) = C2×He3.C6φ: S3×C6/C6S3 ⊆ Aut C32543C3^2.2(S3xC6)324,70
C32.3(S3×C6) = C2×He3.2C6φ: S3×C6/C6S3 ⊆ Aut C32543C3^2.3(S3xC6)324,72
C32.4(S3×C6) = C2×He3.4C6φ: S3×C6/C6S3 ⊆ Aut C32543C3^2.4(S3xC6)324,148
C32.5(S3×C6) = C2×C33⋊C6φ: S3×C6/C6C6 ⊆ Aut C32186+C3^2.5(S3xC6)324,69
C32.6(S3×C6) = C2×He3.S3φ: S3×C6/C6C6 ⊆ Aut C32546+C3^2.6(S3xC6)324,71
C32.7(S3×C6) = C2×He3.2S3φ: S3×C6/C6C6 ⊆ Aut C32546+C3^2.7(S3xC6)324,73
C32.8(S3×C6) = C2×He3.4S3φ: S3×C6/C6C6 ⊆ Aut C32546+C3^2.8(S3xC6)324,147
C32.9(S3×C6) = C3×S3×D9φ: S3×C6/C32C22 ⊆ Aut C32364C3^2.9(S3xC6)324,114
C32.10(S3×C6) = S3×C9⋊C6φ: S3×C6/C32C22 ⊆ Aut C321812+C3^2.10(S3xC6)324,118
C32.11(S3×C6) = C2×S3×3- 1+2φ: S3×C6/D6C3 ⊆ Aut C32366C3^2.11(S3xC6)324,141
C32.12(S3×C6) = S32×C9φ: S3×C6/C3×S3C2 ⊆ Aut C32364C3^2.12(S3xC6)324,115
C32.13(S3×C6) = D9×C18φ: S3×C6/C3×C6C2 ⊆ Aut C32362C3^2.13(S3xC6)324,61
C32.14(S3×C6) = C2×C32⋊C18φ: S3×C6/C3×C6C2 ⊆ Aut C32366C3^2.14(S3xC6)324,62
C32.15(S3×C6) = C2×C32⋊D9φ: S3×C6/C3×C6C2 ⊆ Aut C3254C3^2.15(S3xC6)324,63
C32.16(S3×C6) = C2×C9⋊C18φ: S3×C6/C3×C6C2 ⊆ Aut C32366C3^2.16(S3xC6)324,64
C32.17(S3×C6) = D9×C3×C6φ: S3×C6/C3×C6C2 ⊆ Aut C32108C3^2.17(S3xC6)324,136
C32.18(S3×C6) = C6×C9⋊C6φ: S3×C6/C3×C6C2 ⊆ Aut C32366C3^2.18(S3xC6)324,140
C32.19(S3×C6) = C6×C9⋊S3φ: S3×C6/C3×C6C2 ⊆ Aut C32108C3^2.19(S3xC6)324,142
C32.20(S3×C6) = C18×C3⋊S3φ: S3×C6/C3×C6C2 ⊆ Aut C32108C3^2.20(S3xC6)324,143
C32.21(S3×C6) = C2×C33.S3φ: S3×C6/C3×C6C2 ⊆ Aut C3254C3^2.21(S3xC6)324,146
C32.22(S3×C6) = S3×C3×C18central extension (φ=1)108C3^2.22(S3xC6)324,137

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