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Extensions 1→N→G→Q→1 with N=C33 and Q=C3×S3

Direct product G=N×Q with N=C33 and Q=C3×S3
dρLabelID
S3×C34162S3xC3^4486,256

Semidirect products G=N:Q with N=C33 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
C33⋊1(C3×S3) = C34⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3:1(C3xS3)486,102
C33⋊2(C3×S3) = C3≀C3⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3:2(C3xS3)486,126
C33⋊3(C3×S3) = C34⋊3S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3:3(C3xS3)486,145
C33⋊4(C3×S3) = C33⋊(C3×S3)φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3:4(C3xS3)486,176
C33⋊5(C3×S3) = 3+ 1+4⋊C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3:5(C3xS3)486,236
C33⋊6(C3×S3) = 3+ 1+4⋊2C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3:6(C3xS3)486,237
C33⋊7(C3×S3) = C3×C3≀S3φ: C3×S3/C3 → S3 ⊆ Aut C3327C3^3:7(C3xS3)486,115
C33⋊8(C3×S3) = C3×C33⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C33186C3^3:8(C3xS3)486,165
C33⋊9(C3×S3) = C32×C32⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C3354C3^3:9(C3xS3)486,222
C33⋊10(C3×S3) = C32×He3⋊C2φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3:10(C3xS3)486,230
C33⋊11(C3×S3) = C3×He3⋊5S3φ: C3×S3/C3 → S3 ⊆ Aut C3354C3^3:11(C3xS3)486,243
C33⋊12(C3×S3) = C34⋊5C6φ: C3×S3/C3 → C6 ⊆ Aut C3327C3^3:12(C3xS3)486,167
C33⋊13(C3×S3) = C3×He3⋊4S3φ: C3×S3/C3 → C6 ⊆ Aut C3354C3^3:13(C3xS3)486,229
C33⋊14(C3×S3) = C3⋊S3×He3φ: C3×S3/C3 → C6 ⊆ Aut C3354C3^3:14(C3xS3)486,231
C33⋊15(C3×S3) = C34⋊10C6φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3:15(C3xS3)486,242
C33⋊16(C3×S3) = S3×C3≀C3φ: C3×S3/S3 → C3 ⊆ Aut C33186C3^3:16(C3xS3)486,117
C33⋊17(C3×S3) = C3×S3×He3φ: C3×S3/S3 → C3 ⊆ Aut C3354C3^3:17(C3xS3)486,223
C33⋊18(C3×S3) = C3⋊S3×C33φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3:18(C3xS3)486,257
C33⋊19(C3×S3) = C32×C33⋊C2φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3:19(C3xS3)486,258
C33⋊20(C3×S3) = C3×C34⋊C2φ: C3×S3/C32 → C2 ⊆ Aut C33162C3^3:20(C3xS3)486,259

Non-split extensions G=N.Q with N=C33 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
C33.1(C3×S3) = C3.C3≀S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.1(C3xS3)486,4
C33.2(C3×S3) = C32⋊C9.S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3.2(C3xS3)486,5
C33.3(C3×S3) = C32⋊C9⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3.3(C3xS3)486,6
C33.4(C3×S3) = C32⋊C9⋊S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3.4(C3xS3)486,7
C33.5(C3×S3) = C3.3C3≀S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.5(C3xS3)486,8
C33.6(C3×S3) = (C3×He3).C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.6(C3xS3)486,9
C33.7(C3×S3) = C32⋊C9.C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.7(C3xS3)486,10
C33.8(C3×S3) = C33.(C3×S3)φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.8(C3xS3)486,11
C33.9(C3×S3) = C32⋊2D9.C3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.9(C3xS3)486,12
C33.10(C3×S3) = D9⋊He3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.10(C3xS3)486,106
C33.11(C3×S3) = C9⋊He3⋊C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.11(C3xS3)486,107
C33.12(C3×S3) = C92⋊7C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.12(C3xS3)486,109
C33.13(C3×S3) = C92⋊8C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3.13(C3xS3)486,110
C33.14(C3×S3) = (C3×He3)⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3.14(C3xS3)486,127
C33.15(C3×S3) = He3.C3⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3.15(C3xS3)486,128
C33.16(C3×S3) = C9⋊S3⋊C32φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3.16(C3xS3)486,129
C33.17(C3×S3) = He3.(C3×C6)φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3.17(C3xS3)486,130
C33.18(C3×S3) = He3.(C3×S3)φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3.18(C3xS3)486,131
C33.19(C3×S3) = C3≀C3.C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3.19(C3xS3)486,132
C33.20(C3×S3) = (C32×C9)⋊S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.20(C3xS3)486,149
C33.21(C3×S3) = (C32×C9)⋊8S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.21(C3xS3)486,150
C33.22(C3×S3) = C92⋊6S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33186C3^3.22(C3xS3)486,153
C33.23(C3×S3) = C92⋊5S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C33546C3^3.23(C3xS3)486,156
C33.24(C3×S3) = 3- 1+4⋊C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C332718+C3^3.24(C3xS3)486,238
C33.25(C3×S3) = 3- 1+4⋊2C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C33279C3^3.25(C3xS3)486,239
C33.26(C3×S3) = C33⋊1D9φ: C3×S3/C3 → S3 ⊆ Aut C33186C3^3.26(C3xS3)486,19
C33.27(C3×S3) = (C3×C9)⋊D9φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.27(C3xS3)486,21
C33.28(C3×S3) = (C3×C9)⋊3D9φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.28(C3xS3)486,23
C33.29(C3×S3) = He3⋊C18φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3.29(C3xS3)486,24
C33.30(C3×S3) = C3×C32⋊D9φ: C3×S3/C3 → S3 ⊆ Aut C3354C3^3.30(C3xS3)486,94
C33.31(C3×S3) = C9×C32⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.31(C3xS3)486,98
C33.32(C3×S3) = C9×C9⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.32(C3xS3)486,100
C33.33(C3×S3) = C34⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C3327C3^3.33(C3xS3)486,103
C33.34(C3×S3) = C34.S3φ: C3×S3/C3 → S3 ⊆ Aut C3327C3^3.34(C3xS3)486,105
C33.35(C3×S3) = C3×He3.C6φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3.35(C3xS3)486,118
C33.36(C3×S3) = C3×He3.2C6φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3.36(C3xS3)486,121
C33.37(C3×S3) = C3≀S3⋊3C3φ: C3×S3/C3 → S3 ⊆ Aut C33273C3^3.37(C3xS3)486,125
C33.38(C3×S3) = C3×C32⋊2D9φ: C3×S3/C3 → S3 ⊆ Aut C3354C3^3.38(C3xS3)486,135
C33.39(C3×S3) = C92⋊4S3φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.39(C3xS3)486,140
C33.40(C3×S3) = C9×He3⋊C2φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3.40(C3xS3)486,143
C33.41(C3×S3) = C34.7S3φ: C3×S3/C3 → S3 ⊆ Aut C33186C3^3.41(C3xS3)486,147
C33.42(C3×S3) = C9⋊C9⋊2S3φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.42(C3xS3)486,152
C33.43(C3×S3) = C34⋊5S3φ: C3×S3/C3 → S3 ⊆ Aut C33186C3^3.43(C3xS3)486,166
C33.44(C3×S3) = He3.C3⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.44(C3xS3)486,169
C33.45(C3×S3) = He3⋊C3⋊2S3φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.45(C3xS3)486,172
C33.46(C3×S3) = C32×C9⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C3354C3^3.46(C3xS3)486,224
C33.47(C3×S3) = C3×He3.4C6φ: C3×S3/C3 → S3 ⊆ Aut C3381C3^3.47(C3xS3)486,235
C33.48(C3×S3) = C9○He3⋊4S3φ: C3×S3/C3 → S3 ⊆ Aut C33546C3^3.48(C3xS3)486,246
C33.49(C3×S3) = C33⋊1C18φ: C3×S3/C3 → C6 ⊆ Aut C33186C3^3.49(C3xS3)486,18
C33.50(C3×S3) = (C3×C9)⋊C18φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.50(C3xS3)486,20
C33.51(C3×S3) = C9⋊S3⋊3C9φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.51(C3xS3)486,22
C33.52(C3×S3) = He3⋊D9φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.52(C3xS3)486,25
C33.53(C3×S3) = D9×He3φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.53(C3xS3)486,99
C33.54(C3×S3) = D9×3- 1+2φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.54(C3xS3)486,101
C33.55(C3×S3) = C34.C6φ: C3×S3/C3 → C6 ⊆ Aut C33186C3^3.55(C3xS3)486,104
C33.56(C3×S3) = D9⋊3- 1+2φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.56(C3xS3)486,108
C33.57(C3×S3) = C3×C33⋊C6φ: C3×S3/C3 → C6 ⊆ Aut C33186C3^3.57(C3xS3)486,116
C33.58(C3×S3) = C3×He3.S3φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.58(C3xS3)486,119
C33.59(C3×S3) = C3×He3.2S3φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.59(C3xS3)486,122
C33.60(C3×S3) = C92⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.60(C3xS3)486,139
C33.61(C3×S3) = He3⋊3D9φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.61(C3xS3)486,142
C33.62(C3×S3) = C34⋊4C6φ: C3×S3/C3 → C6 ⊆ Aut C3327C3^3.62(C3xS3)486,146
C33.63(C3×S3) = C9⋊He3⋊2C2φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.63(C3xS3)486,148
C33.64(C3×S3) = (C32×C9)⋊C6φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.64(C3xS3)486,151
C33.65(C3×S3) = C32⋊4D9⋊C3φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.65(C3xS3)486,170
C33.66(C3×S3) = He3⋊C3⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.66(C3xS3)486,173
C33.67(C3×S3) = C3≀C3.S3φ: C3×S3/C3 → C6 ⊆ Aut C33276+C3^3.67(C3xS3)486,175
C33.68(C3×S3) = C3⋊S3×3- 1+2φ: C3×S3/C3 → C6 ⊆ Aut C3354C3^3.68(C3xS3)486,233
C33.69(C3×S3) = C3×He3.4S3φ: C3×S3/C3 → C6 ⊆ Aut C33546C3^3.69(C3xS3)486,234
C33.70(C3×S3) = C9○He3⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C3381C3^3.70(C3xS3)486,245
C33.71(C3×S3) = S3×C32⋊C9φ: C3×S3/S3 → C3 ⊆ Aut C3354C3^3.71(C3xS3)486,95
C33.72(C3×S3) = C3×S3×3- 1+2φ: C3×S3/S3 → C3 ⊆ Aut C3354C3^3.72(C3xS3)486,225
C33.73(C3×S3) = C9⋊S3⋊C9φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.73(C3xS3)486,3
C33.74(C3×S3) = D9×C3×C9φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.74(C3xS3)486,91
C33.75(C3×S3) = C3×C32⋊C18φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.75(C3xS3)486,93
C33.76(C3×S3) = C3×C9⋊C18φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.76(C3xS3)486,96
C33.77(C3×S3) = C9×C9⋊S3φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.77(C3xS3)486,133
C33.78(C3×S3) = C33⋊C18φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.78(C3xS3)486,136
C33.79(C3×S3) = C33⋊D9φ: C3×S3/C32 → C2 ⊆ Aut C3381C3^3.79(C3xS3)486,137
C33.80(C3×S3) = C9⋊(S3×C9)φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.80(C3xS3)486,138
C33.81(C3×S3) = D9×C33φ: C3×S3/C32 → C2 ⊆ Aut C33162C3^3.81(C3xS3)486,220
C33.82(C3×S3) = C32×C9⋊S3φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.82(C3xS3)486,227
C33.83(C3×S3) = C3⋊S3×C3×C9φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.83(C3xS3)486,228
C33.84(C3×S3) = C3×C33.S3φ: C3×S3/C32 → C2 ⊆ Aut C3354C3^3.84(C3xS3)486,232
C33.85(C3×S3) = C3×C32⋊4D9φ: C3×S3/C32 → C2 ⊆ Aut C33162C3^3.85(C3xS3)486,240
C33.86(C3×S3) = C9×C33⋊C2φ: C3×S3/C32 → C2 ⊆ Aut C33162C3^3.86(C3xS3)486,241
C33.87(C3×S3) = C34.11S3φ: C3×S3/C32 → C2 ⊆ Aut C3381C3^3.87(C3xS3)486,244
C33.88(C3×S3) = S3×C32×C9central extension (φ=1)162C3^3.88(C3xS3)486,221

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