# Extensions 1→N→G→Q→1 with N=C33 and Q=C3×C6

Direct product G=N×Q with N=C33 and Q=C3×C6
dρLabelID
C34×C6486C3^4xC6486,261

Semidirect products G=N:Q with N=C33 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C331(C3×C6) = C34⋊S3φ: C3×C6/C1C3×C6 ⊆ Aut C3327C3^3:1(C3xC6)486,103
C332(C3×C6) = (C3×He3)⋊C6φ: C3×C6/C1C3×C6 ⊆ Aut C332718+C3^3:2(C3xC6)486,127
C333(C3×C6) = 3+ 1+4⋊C2φ: C3×C6/C1C3×C6 ⊆ Aut C332718+C3^3:3(C3xC6)486,236
C334(C3×C6) = C2×C32⋊He3φ: C3×C6/C2C32 ⊆ Aut C3354C3^3:4(C3xC6)486,196
C335(C3×C6) = C2×C33⋊C32φ: C3×C6/C2C32 ⊆ Aut C33549C3^3:5(C3xC6)486,215
C336(C3×C6) = C2×3+ 1+4φ: C3×C6/C2C32 ⊆ Aut C33549C3^3:6(C3xC6)486,254
C337(C3×C6) = C3×C33⋊C6φ: C3×C6/C3C6 ⊆ Aut C33186C3^3:7(C3xC6)486,116
C338(C3×C6) = C32×C32⋊C6φ: C3×C6/C3C6 ⊆ Aut C3354C3^3:8(C3xC6)486,222
C339(C3×C6) = C3×S3×He3φ: C3×C6/C3C6 ⊆ Aut C3354C3^3:9(C3xC6)486,223
C3310(C3×C6) = C3×He34S3φ: C3×C6/C3C6 ⊆ Aut C3354C3^3:10(C3xC6)486,229
C3311(C3×C6) = C6×C3≀C3φ: C3×C6/C6C3 ⊆ Aut C3354C3^3:11(C3xC6)486,210
C3312(C3×C6) = C3×C6×He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3:12(C3xC6)486,251
C3313(C3×C6) = S3×C34φ: C3×C6/C32C2 ⊆ Aut C33162C3^3:13(C3xC6)486,256
C3314(C3×C6) = C3⋊S3×C33φ: C3×C6/C32C2 ⊆ Aut C3354C3^3:14(C3xC6)486,257
C3315(C3×C6) = C32×C33⋊C2φ: C3×C6/C32C2 ⊆ Aut C3354C3^3:15(C3xC6)486,258

Non-split extensions G=N.Q with N=C33 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C33.1(C3×C6) = C2×C32.24He3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.1(C3xC6)486,63
C33.2(C3×C6) = C2×C33.C32φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.2(C3xC6)486,64
C33.3(C3×C6) = C2×C33.3C32φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.3(C3xC6)486,65
C33.4(C3×C6) = C2×C32.27He3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.4(C3xC6)486,66
C33.5(C3×C6) = C2×C32.28He3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.5(C3xC6)486,67
C33.6(C3×C6) = C2×C32.29He3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.6(C3xC6)486,68
C33.7(C3×C6) = C2×C33.7C32φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.7(C3xC6)486,69
C33.8(C3×C6) = C2×C9⋊He3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.8(C3xC6)486,198
C33.9(C3×C6) = C2×C32.23C33φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.9(C3xC6)486,199
C33.10(C3×C6) = C2×C927C3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.10(C3xC6)486,202
C33.11(C3×C6) = C2×C924C3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.11(C3xC6)486,203
C33.12(C3×C6) = C2×C925C3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.12(C3xC6)486,204
C33.13(C3×C6) = C2×C928C3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.13(C3xC6)486,205
C33.14(C3×C6) = C2×C929C3φ: C3×C6/C2C32 ⊆ Aut C33162C3^3.14(C3xC6)486,206
C33.15(C3×C6) = C2×He3.C32φ: C3×C6/C2C32 ⊆ Aut C33549C3^3.15(C3xC6)486,216
C33.16(C3×C6) = C2×He3⋊C32φ: C3×C6/C2C32 ⊆ Aut C33549C3^3.16(C3xC6)486,217
C33.17(C3×C6) = C2×C32.C33φ: C3×C6/C2C32 ⊆ Aut C33549C3^3.17(C3xC6)486,218
C33.18(C3×C6) = C2×C9.2He3φ: C3×C6/C2C32 ⊆ Aut C33549C3^3.18(C3xC6)486,219
C33.19(C3×C6) = C2×3- 1+4φ: C3×C6/C2C32 ⊆ Aut C33549C3^3.19(C3xC6)486,255
C33.20(C3×C6) = C3×C32⋊C18φ: C3×C6/C3C6 ⊆ Aut C3354C3^3.20(C3xC6)486,93
C33.21(C3×C6) = C9×C32⋊C6φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.21(C3xC6)486,98
C33.22(C3×C6) = C34⋊C6φ: C3×C6/C3C6 ⊆ Aut C33186C3^3.22(C3xC6)486,102
C33.23(C3×C6) = C34.C6φ: C3×C6/C3C6 ⊆ Aut C33186C3^3.23(C3xC6)486,104
C33.24(C3×C6) = C9⋊He3⋊C2φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.24(C3xC6)486,107
C33.25(C3×C6) = S3×C3≀C3φ: C3×C6/C3C6 ⊆ Aut C33186C3^3.25(C3xC6)486,117
C33.26(C3×C6) = S3×He3.C3φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.26(C3xC6)486,120
C33.27(C3×C6) = S3×He3⋊C3φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.27(C3xC6)486,123
C33.28(C3×C6) = S3×C3.He3φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.28(C3xC6)486,124
C33.29(C3×C6) = C3×S3×3- 1+2φ: C3×C6/C3C6 ⊆ Aut C3354C3^3.29(C3xC6)486,225
C33.30(C3×C6) = S3×C9○He3φ: C3×C6/C3C6 ⊆ Aut C33546C3^3.30(C3xC6)486,226
C33.31(C3×C6) = C2×C33⋊C9φ: C3×C6/C6C3 ⊆ Aut C3354C3^3.31(C3xC6)486,73
C33.32(C3×C6) = C2×C32.19He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.32(C3xC6)486,74
C33.33(C3×C6) = C2×C32.20He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.33(C3xC6)486,75
C33.34(C3×C6) = C2×He3⋊C9φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.34(C3xC6)486,77
C33.35(C3×C6) = C2×3- 1+2⋊C9φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.35(C3xC6)486,78
C33.36(C3×C6) = C6×C32⋊C9φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.36(C3xC6)486,191
C33.37(C3×C6) = C2×C923C3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.37(C3xC6)486,193
C33.38(C3×C6) = C18×He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.38(C3xC6)486,194
C33.39(C3×C6) = C18×3- 1+2φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.39(C3xC6)486,195
C33.40(C3×C6) = C2×C34.C3φ: C3×C6/C6C3 ⊆ Aut C3354C3^3.40(C3xC6)486,197
C33.41(C3×C6) = C2×C9⋊3- 1+2φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.41(C3xC6)486,200
C33.42(C3×C6) = C2×C33.31C32φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.42(C3xC6)486,201
C33.43(C3×C6) = C6×He3.C3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.43(C3xC6)486,211
C33.44(C3×C6) = C6×He3⋊C3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.44(C3xC6)486,212
C33.45(C3×C6) = C6×C3.He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.45(C3xC6)486,213
C33.46(C3×C6) = C2×C9.He3φ: C3×C6/C6C3 ⊆ Aut C33543C3^3.46(C3xC6)486,214
C33.47(C3×C6) = C3×C6×3- 1+2φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.47(C3xC6)486,252
C33.48(C3×C6) = C6×C9○He3φ: C3×C6/C6C3 ⊆ Aut C33162C3^3.48(C3xC6)486,253
C33.49(C3×C6) = S3×C92φ: C3×C6/C32C2 ⊆ Aut C33162C3^3.49(C3xC6)486,92
C33.50(C3×C6) = S3×C32⋊C9φ: C3×C6/C32C2 ⊆ Aut C3354C3^3.50(C3xC6)486,95
C33.51(C3×C6) = S3×C9⋊C9φ: C3×C6/C32C2 ⊆ Aut C33162C3^3.51(C3xC6)486,97
C33.52(C3×C6) = S3×C32×C9φ: C3×C6/C32C2 ⊆ Aut C33162C3^3.52(C3xC6)486,221
C33.53(C3×C6) = C3⋊S3×C3×C9φ: C3×C6/C32C2 ⊆ Aut C3354C3^3.53(C3xC6)486,228
C33.54(C3×C6) = C3⋊S3×He3φ: C3×C6/C32C2 ⊆ Aut C3354C3^3.54(C3xC6)486,231
C33.55(C3×C6) = C3⋊S3×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C3354C3^3.55(C3xC6)486,233
C33.56(C3×C6) = C2×C3.C92central extension (φ=1)486C3^3.56(C3xC6)486,62
C33.57(C3×C6) = C6×C9⋊C9central extension (φ=1)486C3^3.57(C3xC6)486,192

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