# Extensions 1→N→G→Q→1 with N=C32 and Q=C3×C3⋊S3

Direct product G=N×Q with N=C32 and Q=C3×C3⋊S3
dρLabelID
C3⋊S3×C3354C3:S3xC3^3486,257

Semidirect products G=N:Q with N=C32 and Q=C3×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C321(C3×C3⋊S3) = C3×He34S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C3254C3^2:1(C3xC3:S3)486,229
C322(C3×C3⋊S3) = C3×He35S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C3254C3^2:2(C3xC3:S3)486,243
C323(C3×C3⋊S3) = C3410C6φ: C3×C3⋊S3/C32C6 ⊆ Aut C3281C3^2:3(C3xC3:S3)486,242
C324(C3×C3⋊S3) = C3⋊S3×He3φ: C3×C3⋊S3/C3⋊S3C3 ⊆ Aut C3254C3^2:4(C3xC3:S3)486,231
C325(C3×C3⋊S3) = C32×C33⋊C2φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2:5(C3xC3:S3)486,258
C326(C3×C3⋊S3) = C3×C34⋊C2φ: C3×C3⋊S3/C33C2 ⊆ Aut C32162C3^2:6(C3xC3:S3)486,259

Non-split extensions G=N.Q with N=C32 and Q=C3×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C32.1(C3×C3⋊S3) = C3×C33⋊S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32186C3^2.1(C3xC3:S3)486,165
C32.2(C3×C3⋊S3) = C345S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32186C3^2.2(C3xC3:S3)486,166
C32.3(C3×C3⋊S3) = C3×He3.3S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.3(C3xC3:S3)486,168
C32.4(C3×C3⋊S3) = He3.C3⋊S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.4(C3xC3:S3)486,169
C32.5(C3×C3⋊S3) = C3×He3⋊S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.5(C3xC3:S3)486,171
C32.6(C3×C3⋊S3) = He3⋊C32S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.6(C3xC3:S3)486,172
C32.7(C3×C3⋊S3) = C3×3- 1+2.S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.7(C3xC3:S3)486,174
C32.8(C3×C3⋊S3) = C33⋊(C3×S3)φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.8(C3xC3:S3)486,176
C32.9(C3×C3⋊S3) = He3.C32C6φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.9(C3xC3:S3)486,177
C32.10(C3×C3⋊S3) = He3⋊(C3×S3)φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.10(C3xC3:S3)486,178
C32.11(C3×C3⋊S3) = C3.He3⋊C6φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.11(C3xC3:S3)486,179
C32.12(C3×C3⋊S3) = C3×He3.4S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.12(C3xC3:S3)486,234
C32.13(C3×C3⋊S3) = 3+ 1+4⋊C2φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.13(C3xC3:S3)486,236
C32.14(C3×C3⋊S3) = 3- 1+4⋊C2φ: C3×C3⋊S3/C32S3 ⊆ Aut C322718+C3^2.14(C3xC3:S3)486,238
C32.15(C3×C3⋊S3) = C9○He34S3φ: C3×C3⋊S3/C32S3 ⊆ Aut C32546C3^2.15(C3xC3:S3)486,246
C32.16(C3×C3⋊S3) = C345C6φ: C3×C3⋊S3/C32C6 ⊆ Aut C3227C3^2.16(C3xC3:S3)486,167
C32.17(C3×C3⋊S3) = C324D9⋊C3φ: C3×C3⋊S3/C32C6 ⊆ Aut C3281C3^2.17(C3xC3:S3)486,170
C32.18(C3×C3⋊S3) = He3⋊C33S3φ: C3×C3⋊S3/C32C6 ⊆ Aut C3281C3^2.18(C3xC3:S3)486,173
C32.19(C3×C3⋊S3) = C3≀C3.S3φ: C3×C3⋊S3/C32C6 ⊆ Aut C32276+C3^2.19(C3xC3:S3)486,175
C32.20(C3×C3⋊S3) = C9○He33S3φ: C3×C3⋊S3/C32C6 ⊆ Aut C3281C3^2.20(C3xC3:S3)486,245
C32.21(C3×C3⋊S3) = C3⋊S3×3- 1+2φ: C3×C3⋊S3/C3⋊S3C3 ⊆ Aut C3254C3^2.21(C3xC3:S3)486,233
C32.22(C3×C3⋊S3) = 3+ 1+42C2φ: C3×C3⋊S3/C3⋊S3C3 ⊆ Aut C32279C3^2.22(C3xC3:S3)486,237
C32.23(C3×C3⋊S3) = 3- 1+42C2φ: C3×C3⋊S3/C3⋊S3C3 ⊆ Aut C32279C3^2.23(C3xC3:S3)486,239
C32.24(C3×C3⋊S3) = C9×C9⋊S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.24(C3xC3:S3)486,133
C32.25(C3×C3⋊S3) = C3×C9⋊D9φ: C3×C3⋊S3/C33C2 ⊆ Aut C32162C3^2.25(C3xC3:S3)486,134
C32.26(C3×C3⋊S3) = C3×C322D9φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.26(C3xC3:S3)486,135
C32.27(C3×C3⋊S3) = C33⋊C18φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.27(C3xC3:S3)486,136
C32.28(C3×C3⋊S3) = C33⋊D9φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.28(C3xC3:S3)486,137
C32.29(C3×C3⋊S3) = C9⋊(S3×C9)φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.29(C3xC3:S3)486,138
C32.30(C3×C3⋊S3) = C923S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.30(C3xC3:S3)486,139
C32.31(C3×C3⋊S3) = C924S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.31(C3xC3:S3)486,140
C32.32(C3×C3⋊S3) = C923C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.32(C3xC3:S3)486,141
C32.33(C3×C3⋊S3) = He33D9φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.33(C3xC3:S3)486,142
C32.34(C3×C3⋊S3) = C929C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.34(C3xC3:S3)486,144
C32.35(C3×C3⋊S3) = C343S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32186C3^2.35(C3xC3:S3)486,145
C32.36(C3×C3⋊S3) = C344C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3227C3^2.36(C3xC3:S3)486,146
C32.37(C3×C3⋊S3) = C34.7S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32186C3^2.37(C3xC3:S3)486,147
C32.38(C3×C3⋊S3) = C9⋊He32C2φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.38(C3xC3:S3)486,148
C32.39(C3×C3⋊S3) = (C32×C9)⋊S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.39(C3xC3:S3)486,149
C32.40(C3×C3⋊S3) = (C32×C9)⋊8S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.40(C3xC3:S3)486,150
C32.41(C3×C3⋊S3) = (C32×C9)⋊C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.41(C3xC3:S3)486,151
C32.42(C3×C3⋊S3) = C9⋊C92S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.42(C3xC3:S3)486,152
C32.43(C3×C3⋊S3) = C926S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32186C3^2.43(C3xC3:S3)486,153
C32.44(C3×C3⋊S3) = C9210C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.44(C3xC3:S3)486,154
C32.45(C3×C3⋊S3) = C924C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.45(C3xC3:S3)486,155
C32.46(C3×C3⋊S3) = C925S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C32546C3^2.46(C3xC3:S3)486,156
C32.47(C3×C3⋊S3) = C925C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.47(C3xC3:S3)486,157
C32.48(C3×C3⋊S3) = C9211C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.48(C3xC3:S3)486,158
C32.49(C3×C3⋊S3) = C9212C6φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.49(C3xC3:S3)486,159
C32.50(C3×C3⋊S3) = C32×C9⋊S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.50(C3xC3:S3)486,227
C32.51(C3×C3⋊S3) = C3×C33.S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C3254C3^2.51(C3xC3:S3)486,232
C32.52(C3×C3⋊S3) = C3×C324D9φ: C3×C3⋊S3/C33C2 ⊆ Aut C32162C3^2.52(C3xC3:S3)486,240
C32.53(C3×C3⋊S3) = C9×C33⋊C2φ: C3×C3⋊S3/C33C2 ⊆ Aut C32162C3^2.53(C3xC3:S3)486,241
C32.54(C3×C3⋊S3) = C34.11S3φ: C3×C3⋊S3/C33C2 ⊆ Aut C3281C3^2.54(C3xC3:S3)486,244
C32.55(C3×C3⋊S3) = C9×He3⋊C2central extension (φ=1)81C3^2.55(C3xC3:S3)486,143
C32.56(C3×C3⋊S3) = C3⋊S3×C3×C9central extension (φ=1)54C3^2.56(C3xC3:S3)486,228
C32.57(C3×C3⋊S3) = C32×He3⋊C2central extension (φ=1)81C3^2.57(C3xC3:S3)486,230
C32.58(C3×C3⋊S3) = C3×He3.4C6central extension (φ=1)81C3^2.58(C3xC3:S3)486,235

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