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

Direct product G=N×Q with N=C32 and Q=S3×C32
dρLabelID
S3×C34162S3xC3^4486,256

Semidirect products G=N:Q with N=C32 and Q=S3×C32
extensionφ:Q→Aut NdρLabelID
C321(S3×C32) = C32×C32⋊C6φ: S3×C32/C32S3 ⊆ Aut C3254C3^2:1(S3xC3^2)486,222
C322(S3×C32) = C32×He3⋊C2φ: S3×C32/C32S3 ⊆ Aut C3281C3^2:2(S3xC3^2)486,230
C323(S3×C32) = C3×He34S3φ: S3×C32/C32C6 ⊆ Aut C3254C3^2:3(S3xC3^2)486,229
C324(S3×C32) = C3×S3×He3φ: S3×C32/C3×S3C3 ⊆ Aut C3254C3^2:4(S3xC3^2)486,223
C325(S3×C32) = C3⋊S3×C33φ: S3×C32/C33C2 ⊆ Aut C3254C3^2:5(S3xC3^2)486,257
C326(S3×C32) = C32×C33⋊C2φ: S3×C32/C33C2 ⊆ Aut C3254C3^2:6(S3xC3^2)486,258

Non-split extensions G=N.Q with N=C32 and Q=S3×C32
extensionφ:Q→Aut NdρLabelID
C32.1(S3×C32) = C3×C3≀S3φ: S3×C32/C32S3 ⊆ Aut C3227C3^2.1(S3xC3^2)486,115
C32.2(S3×C32) = C3×He3.C6φ: S3×C32/C32S3 ⊆ Aut C3281C3^2.2(S3xC3^2)486,118
C32.3(S3×C32) = C3×He3.2C6φ: S3×C32/C32S3 ⊆ Aut C3281C3^2.3(S3xC3^2)486,121
C32.4(S3×C32) = C3≀S33C3φ: S3×C32/C32S3 ⊆ Aut C32273C3^2.4(S3xC3^2)486,125
C32.5(S3×C32) = C3≀C3⋊C6φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.5(S3xC3^2)486,126
C32.6(S3×C32) = He3.C3⋊C6φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.6(S3xC3^2)486,128
C32.7(S3×C32) = He3.(C3×C6)φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.7(S3xC3^2)486,130
C32.8(S3×C32) = C3≀C3.C6φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.8(S3xC3^2)486,132
C32.9(S3×C32) = C32×C9⋊C6φ: S3×C32/C32S3 ⊆ Aut C3254C3^2.9(S3xC3^2)486,224
C32.10(S3×C32) = C3×He3.4C6φ: S3×C32/C32S3 ⊆ Aut C3281C3^2.10(S3xC3^2)486,235
C32.11(S3×C32) = 3+ 1+42C2φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.11(S3xC3^2)486,237
C32.12(S3×C32) = 3- 1+42C2φ: S3×C32/C32S3 ⊆ Aut C32279C3^2.12(S3xC3^2)486,239
C32.13(S3×C32) = C3×C33⋊C6φ: S3×C32/C32C6 ⊆ Aut C32186C3^2.13(S3xC3^2)486,116
C32.14(S3×C32) = C3×He3.S3φ: S3×C32/C32C6 ⊆ Aut C32546C3^2.14(S3xC3^2)486,119
C32.15(S3×C32) = C3×He3.2S3φ: S3×C32/C32C6 ⊆ Aut C32546C3^2.15(S3xC3^2)486,122
C32.16(S3×C32) = (C3×He3)⋊C6φ: S3×C32/C32C6 ⊆ Aut C322718+C3^2.16(S3xC3^2)486,127
C32.17(S3×C32) = C9⋊S3⋊C32φ: S3×C32/C32C6 ⊆ Aut C322718+C3^2.17(S3xC3^2)486,129
C32.18(S3×C32) = He3.(C3×S3)φ: S3×C32/C32C6 ⊆ Aut C322718+C3^2.18(S3xC3^2)486,131
C32.19(S3×C32) = C3×He3.4S3φ: S3×C32/C32C6 ⊆ Aut C32546C3^2.19(S3xC3^2)486,234
C32.20(S3×C32) = 3+ 1+4⋊C2φ: S3×C32/C32C6 ⊆ Aut C322718+C3^2.20(S3xC3^2)486,236
C32.21(S3×C32) = 3- 1+4⋊C2φ: S3×C32/C32C6 ⊆ Aut C322718+C3^2.21(S3xC3^2)486,238
C32.22(S3×C32) = S3×C3≀C3φ: S3×C32/C3×S3C3 ⊆ Aut C32186C3^2.22(S3xC3^2)486,117
C32.23(S3×C32) = S3×He3.C3φ: S3×C32/C3×S3C3 ⊆ Aut C32546C3^2.23(S3xC3^2)486,120
C32.24(S3×C32) = S3×He3⋊C3φ: S3×C32/C3×S3C3 ⊆ Aut C32546C3^2.24(S3xC3^2)486,123
C32.25(S3×C32) = S3×C3.He3φ: S3×C32/C3×S3C3 ⊆ Aut C32546C3^2.25(S3xC3^2)486,124
C32.26(S3×C32) = S3×C9○He3φ: S3×C32/C3×S3C3 ⊆ Aut C32546C3^2.26(S3xC3^2)486,226
C32.27(S3×C32) = D9×C3×C9φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.27(S3xC3^2)486,91
C32.28(S3×C32) = C3×C32⋊C18φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.28(S3xC3^2)486,93
C32.29(S3×C32) = C3×C32⋊D9φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.29(S3xC3^2)486,94
C32.30(S3×C32) = C3×C9⋊C18φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.30(S3xC3^2)486,96
C32.31(S3×C32) = C9×C32⋊C6φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.31(S3xC3^2)486,98
C32.32(S3×C32) = D9×He3φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.32(S3xC3^2)486,99
C32.33(S3×C32) = C9×C9⋊C6φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.33(S3xC3^2)486,100
C32.34(S3×C32) = D9×3- 1+2φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.34(S3xC3^2)486,101
C32.35(S3×C32) = C34⋊C6φ: S3×C32/C33C2 ⊆ Aut C32186C3^2.35(S3xC3^2)486,102
C32.36(S3×C32) = C34⋊S3φ: S3×C32/C33C2 ⊆ Aut C3227C3^2.36(S3xC3^2)486,103
C32.37(S3×C32) = C34.C6φ: S3×C32/C33C2 ⊆ Aut C32186C3^2.37(S3xC3^2)486,104
C32.38(S3×C32) = C34.S3φ: S3×C32/C33C2 ⊆ Aut C3227C3^2.38(S3xC3^2)486,105
C32.39(S3×C32) = D9⋊He3φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.39(S3xC3^2)486,106
C32.40(S3×C32) = C9⋊He3⋊C2φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.40(S3xC3^2)486,107
C32.41(S3×C32) = D9⋊3- 1+2φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.41(S3xC3^2)486,108
C32.42(S3×C32) = C927C6φ: S3×C32/C33C2 ⊆ Aut C32546C3^2.42(S3xC3^2)486,109
C32.43(S3×C32) = C928C6φ: S3×C32/C33C2 ⊆ Aut C32186C3^2.43(S3xC3^2)486,110
C32.44(S3×C32) = D9×C33φ: S3×C32/C33C2 ⊆ Aut C32162C3^2.44(S3xC3^2)486,220
C32.45(S3×C32) = C32×C9⋊S3φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.45(S3xC3^2)486,227
C32.46(S3×C32) = C3⋊S3×C3×C9φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.46(S3xC3^2)486,228
C32.47(S3×C32) = C3⋊S3×He3φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.47(S3xC3^2)486,231
C32.48(S3×C32) = C3×C33.S3φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.48(S3xC3^2)486,232
C32.49(S3×C32) = C3⋊S3×3- 1+2φ: S3×C32/C33C2 ⊆ Aut C3254C3^2.49(S3xC3^2)486,233
C32.50(S3×C32) = S3×C92central extension (φ=1)162C3^2.50(S3xC3^2)486,92
C32.51(S3×C32) = S3×C32⋊C9central extension (φ=1)54C3^2.51(S3xC3^2)486,95
C32.52(S3×C32) = S3×C9⋊C9central extension (φ=1)162C3^2.52(S3xC3^2)486,97
C32.53(S3×C32) = S3×C32×C9central extension (φ=1)162C3^2.53(S3xC3^2)486,221
C32.54(S3×C32) = C3×S3×3- 1+2central extension (φ=1)54C3^2.54(S3xC3^2)486,225

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