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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
C3⋊S3×C3354C3:S3xC3^3486,257

Semidirect products G=N:Q with N=C33 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
C33⋊1(C3⋊S3) = C34⋊4C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3327C3^3:1(C3:S3)486,146
C33⋊2(C3⋊S3) = C34⋊6S3φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3327C3^3:2(C3:S3)486,183
C33⋊3(C3⋊S3) = 3+ 1+4⋊C2φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3:3(C3:S3)486,236
C33⋊4(C3⋊S3) = 3+ 1+4⋊3C2φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C33279C3^3:4(C3:S3)486,249
C33⋊5(C3⋊S3) = C34⋊5S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33186C3^3:5(C3:S3)486,166
C33⋊6(C3⋊S3) = C34⋊7S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3327C3^3:6(C3:S3)486,185
C33⋊7(C3⋊S3) = C3×He3⋊4S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3354C3^3:7(C3:S3)486,229
C33⋊8(C3⋊S3) = C34⋊10C6φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3:8(C3:S3)486,242
C33⋊9(C3⋊S3) = C3×He3⋊5S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3354C3^3:9(C3:S3)486,243
C33⋊10(C3⋊S3) = C34⋊13S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3354C3^3:10(C3:S3)486,248
C33⋊11(C3⋊S3) = C32×C33⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C3354C3^3:11(C3:S3)486,258
C33⋊12(C3⋊S3) = C3×C34⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C33162C3^3:12(C3:S3)486,259
C33⋊13(C3⋊S3) = C35⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C33243C3^3:13(C3:S3)486,260

Non-split extensions G=N.Q with N=C33 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
C33.1(C3⋊S3) = (C3×He3)⋊S3φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.1(C3:S3)486,43
C33.2(C3⋊S3) = (C3×He3).S3φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.2(C3:S3)486,44
C33.3(C3⋊S3) = C33.(C3⋊S3)φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.3(C3:S3)486,45
C33.4(C3⋊S3) = C32⋊C9⋊6S3φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.4(C3:S3)486,46
C33.5(C3⋊S3) = C3.(C33⋊S3)φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.5(C3:S3)486,47
C33.6(C3⋊S3) = C3.(He3⋊S3)φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.6(C3:S3)486,48
C33.7(C3⋊S3) = C32⋊C9.10S3φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.7(C3:S3)486,49
C33.8(C3⋊S3) = C9⋊He3⋊2C2φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.8(C3:S3)486,148
C33.9(C3⋊S3) = (C32×C9)⋊C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.9(C3:S3)486,151
C33.10(C3⋊S3) = C92⋊10C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.10(C3:S3)486,154
C33.11(C3⋊S3) = C92⋊4C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.11(C3:S3)486,155
C33.12(C3⋊S3) = C92⋊5C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.12(C3:S3)486,157
C33.13(C3⋊S3) = C92⋊11C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.13(C3:S3)486,158
C33.14(C3⋊S3) = C92⋊12C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C3381C3^3.14(C3:S3)486,159
C33.15(C3⋊S3) = C33⋊(C3×S3)φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3.15(C3:S3)486,176
C33.16(C3⋊S3) = He3.C3⋊2C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3.16(C3:S3)486,177
C33.17(C3⋊S3) = He3⋊(C3×S3)φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3.17(C3:S3)486,178
C33.18(C3⋊S3) = C3.He3⋊C6φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3.18(C3:S3)486,179
C33.19(C3⋊S3) = 3- 1+4⋊C2φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C332718+C3^3.19(C3:S3)486,238
C33.20(C3⋊S3) = C33⋊2D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3327C3^3.20(C3:S3)486,52
C33.21(C3⋊S3) = (C3×C9)⋊5D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.21(C3:S3)486,53
C33.22(C3⋊S3) = (C3×C9)⋊6D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.22(C3:S3)486,54
C33.23(C3⋊S3) = He3⋊2D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.23(C3:S3)486,56
C33.24(C3⋊S3) = 3- 1+2⋊D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.24(C3:S3)486,57
C33.25(C3⋊S3) = C33⋊D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.25(C3:S3)486,137
C33.26(C3⋊S3) = C92⋊3C6φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.26(C3:S3)486,141
C33.27(C3⋊S3) = He3⋊3D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.27(C3:S3)486,142
C33.28(C3⋊S3) = C92⋊9C6φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.28(C3:S3)486,144
C33.29(C3⋊S3) = C34⋊3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33186C3^3.29(C3:S3)486,145
C33.30(C3⋊S3) = C34.7S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33186C3^3.30(C3:S3)486,147
C33.31(C3⋊S3) = (C32×C9)⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.31(C3:S3)486,149
C33.32(C3⋊S3) = C3×C33⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33186C3^3.32(C3:S3)486,165
C33.33(C3⋊S3) = C3×He3.3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.33(C3:S3)486,168
C33.34(C3⋊S3) = C3×He3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.34(C3:S3)486,171
C33.35(C3⋊S3) = C3×3- 1+2.S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.35(C3:S3)486,174
C33.36(C3⋊S3) = C33⋊6D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3354C3^3.36(C3:S3)486,181
C33.37(C3⋊S3) = He3⋊4D9φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.37(C3:S3)486,182
C33.38(C3⋊S3) = He3.(C3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.38(C3:S3)486,186
C33.39(C3⋊S3) = C3⋊(He3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.39(C3:S3)486,187
C33.40(C3⋊S3) = (C32×C9).S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.40(C3:S3)486,188
C33.41(C3⋊S3) = C3≀C3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33276+C3^3.41(C3:S3)486,189
C33.42(C3⋊S3) = C3×C33.S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3354C3^3.42(C3:S3)486,232
C33.43(C3⋊S3) = C3×He3.4S3φ: C3⋊S3/C3 → S3 ⊆ Aut C33546C3^3.43(C3:S3)486,234
C33.44(C3⋊S3) = C34.11S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.44(C3:S3)486,244
C33.45(C3⋊S3) = C9○He3⋊3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3381C3^3.45(C3:S3)486,245
C33.46(C3⋊S3) = C3.2(C9⋊D9)φ: C3⋊S3/C32 → C2 ⊆ Aut C33162C3^3.46(C3:S3)486,42
C33.47(C3⋊S3) = C3×C9⋊D9φ: C3⋊S3/C32 → C2 ⊆ Aut C33162C3^3.47(C3:S3)486,134
C33.48(C3⋊S3) = C3×C32⋊2D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3354C3^3.48(C3:S3)486,135
C33.49(C3⋊S3) = C92⋊8S3φ: C3⋊S3/C32 → C2 ⊆ Aut C33243C3^3.49(C3:S3)486,180
C33.50(C3⋊S3) = C32×C9⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3354C3^3.50(C3:S3)486,227
C33.51(C3⋊S3) = C3×C32⋊4D9φ: C3⋊S3/C32 → C2 ⊆ Aut C33162C3^3.51(C3:S3)486,240
C33.52(C3⋊S3) = C33⋊9D9φ: C3⋊S3/C32 → C2 ⊆ Aut C33243C3^3.52(C3:S3)486,247
C33.53(C3⋊S3) = C32×He3⋊C2central extension (φ=1)81C3^3.53(C3:S3)486,230

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