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Extensions 1→N→G→Q→1 with N=C3×C9 and Q=C3×S3

Direct product G=N×Q with N=C3×C9 and Q=C3×S3
dρLabelID
S3×C32×C9162S3xC3^2xC9486,221

Semidirect products G=N:Q with N=C3×C9 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C3×C9)⋊1(C3×S3) = C34.7S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9186(C3xC9):1(C3xS3)486,147
(C3×C9)⋊2(C3×S3) = He3.C3⋊2C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9):2(C3xS3)486,177
(C3×C9)⋊3(C3×S3) = He3⋊(C3×S3)φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9):3(C3xS3)486,178
(C3×C9)⋊4(C3×S3) = 3- 1+4⋊C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9):4(C3xS3)486,238
(C3×C9)⋊5(C3×S3) = C34.C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9186(C3xC9):5(C3xS3)486,104
(C3×C9)⋊6(C3×S3) = He3.C3⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9279(C3xC9):6(C3xS3)486,128
(C3×C9)⋊7(C3×S3) = He3.(C3×C6)φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9279(C3xC9):7(C3xS3)486,130
(C3×C9)⋊8(C3×S3) = 3- 1+4⋊2C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9279(C3xC9):8(C3xS3)486,239
(C3×C9)⋊9(C3×S3) = C3×C32⋊C18φ: C3×S3/C3 → S3 ⊆ Aut C3×C954(C3xC9):9(C3xS3)486,93
(C3×C9)⋊10(C3×S3) = C3×He3.C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):10(C3xS3)486,118
(C3×C9)⋊11(C3×S3) = C3×He3.2C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):11(C3xS3)486,121
(C3×C9)⋊12(C3×S3) = C3×C32⋊2D9φ: C3×S3/C3 → S3 ⊆ Aut C3×C954(C3xC9):12(C3xS3)486,135
(C3×C9)⋊13(C3×S3) = C3×He3.3S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):13(C3xS3)486,168
(C3×C9)⋊14(C3×S3) = C3×He3⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):14(C3xS3)486,171
(C3×C9)⋊15(C3×S3) = C3×He3.4S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):15(C3xS3)486,234
(C3×C9)⋊16(C3×S3) = C3×He3.4C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):16(C3xS3)486,235
(C3×C9)⋊17(C3×S3) = C33⋊D9φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9):17(C3xS3)486,137
(C3×C9)⋊18(C3×S3) = C32⋊4D9⋊C3φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9):18(C3xS3)486,170
(C3×C9)⋊19(C3×S3) = He3⋊C3⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9):19(C3xS3)486,173
(C3×C9)⋊20(C3×S3) = C3×C33.S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C954(C3xC9):20(C3xS3)486,232
(C3×C9)⋊21(C3×S3) = C34.11S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9):21(C3xS3)486,244
(C3×C9)⋊22(C3×S3) = C9○He3⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9):22(C3xS3)486,245
(C3×C9)⋊23(C3×S3) = C3⋊S3×3- 1+2φ: C3×S3/C3 → C6 ⊆ Aut C3×C954(C3xC9):23(C3xS3)486,233
(C3×C9)⋊24(C3×S3) = S3×C32⋊C9φ: C3×S3/S3 → C3 ⊆ Aut C3×C954(C3xC9):24(C3xS3)486,95
(C3×C9)⋊25(C3×S3) = S3×He3.C3φ: C3×S3/S3 → C3 ⊆ Aut C3×C9546(C3xC9):25(C3xS3)486,120
(C3×C9)⋊26(C3×S3) = S3×He3⋊C3φ: C3×S3/S3 → C3 ⊆ Aut C3×C9546(C3xC9):26(C3xS3)486,123
(C3×C9)⋊27(C3×S3) = C3×S3×3- 1+2φ: C3×S3/S3 → C3 ⊆ Aut C3×C954(C3xC9):27(C3xS3)486,225
(C3×C9)⋊28(C3×S3) = S3×C9○He3φ: C3×S3/S3 → C3 ⊆ Aut C3×C9546(C3xC9):28(C3xS3)486,226
(C3×C9)⋊29(C3×S3) = C3⋊S3×C3×C9φ: C3×S3/C32 → C2 ⊆ Aut C3×C954(C3xC9):29(C3xS3)486,228
(C3×C9)⋊30(C3×S3) = C32×C9⋊S3φ: C3×S3/C32 → C2 ⊆ Aut C3×C954(C3xC9):30(C3xS3)486,227
(C3×C9)⋊31(C3×S3) = C3×C32⋊4D9φ: C3×S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9):31(C3xS3)486,240

Non-split extensions G=N.Q with N=C3×C9 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C3×C9).1(C3×S3) = C27⋊C18φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9).1(C3xS3)486,31
(C3×C9).2(C3×S3) = C9⋊C9.S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9).2(C3xS3)486,39
(C3×C9).3(C3×S3) = C9⋊C9.3S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9).3(C3xS3)486,40
(C3×C9).4(C3×S3) = C9⋊C9⋊S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9).4(C3xS3)486,41
(C3×C9).5(C3×S3) = C9⋊C9⋊2S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9546(C3xC9).5(C3xS3)486,152
(C3×C9).6(C3×S3) = C92⋊6S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9186(C3xC9).6(C3xS3)486,153
(C3×C9).7(C3×S3) = C92⋊5S3φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9546(C3xC9).7(C3xS3)486,156
(C3×C9).8(C3×S3) = C3.He3⋊C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C92718+(C3xC9).8(C3xS3)486,179
(C3×C9).9(C3×S3) = C9⋊He3⋊C2φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9546(C3xC9).9(C3xS3)486,107
(C3×C9).10(C3×S3) = D9⋊3- 1+2φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9546(C3xC9).10(C3xS3)486,108
(C3×C9).11(C3×S3) = C92⋊7C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9546(C3xC9).11(C3xS3)486,109
(C3×C9).12(C3×S3) = C92⋊8C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9186(C3xC9).12(C3xS3)486,110
(C3×C9).13(C3×S3) = C3≀C3.C6φ: C3×S3/C1 → C3×S3 ⊆ Aut C3×C9279(C3xC9).13(C3xS3)486,132
(C3×C9).14(C3×S3) = C3×C9⋊C18φ: C3×S3/C3 → S3 ⊆ Aut C3×C954(C3xC9).14(C3xS3)486,96
(C3×C9).15(C3×S3) = C9×C32⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).15(C3xS3)486,98
(C3×C9).16(C3×S3) = C9×C9⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).16(C3xS3)486,100
(C3×C9).17(C3×S3) = C92⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9276+(C3xC9).17(C3xS3)486,36
(C3×C9).18(C3×S3) = C92.S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9276+(C3xC9).18(C3xS3)486,38
(C3×C9).19(C3×S3) = C92⋊4S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).19(C3xS3)486,140
(C3×C9).20(C3×S3) = (C32×C9)⋊S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).20(C3xS3)486,149
(C3×C9).21(C3×S3) = C3×3- 1+2.S3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).21(C3xS3)486,174
(C3×C9).22(C3×S3) = C3×C27⋊C6φ: C3×S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).22(C3xS3)486,113
(C3×C9).23(C3×S3) = He3.C18φ: C3×S3/C3 → S3 ⊆ Aut C3×C9813(C3xC9).23(C3xS3)486,26
(C3×C9).24(C3×S3) = He3.2C18φ: C3×S3/C3 → S3 ⊆ Aut C3×C9813(C3xC9).24(C3xS3)486,28
(C3×C9).25(C3×S3) = C3≀S3⋊3C3φ: C3×S3/C3 → S3 ⊆ Aut C3×C9273(C3xC9).25(C3xS3)486,125
(C3×C9).26(C3×S3) = He3.5C18φ: C3×S3/C3 → S3 ⊆ Aut C3×C9813(C3xC9).26(C3xS3)486,164
(C3×C9).27(C3×S3) = C92⋊C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C9276+(C3xC9).27(C3xS3)486,35
(C3×C9).28(C3×S3) = C92⋊2C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C9276+(C3xC9).28(C3xS3)486,37
(C3×C9).29(C3×S3) = C92⋊3C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).29(C3xS3)486,141
(C3×C9).30(C3×S3) = C9⋊He3⋊2C2φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).30(C3xS3)486,148
(C3×C9).31(C3×S3) = (C32×C9)⋊C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).31(C3xS3)486,151
(C3×C9).32(C3×S3) = C92⋊4C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).32(C3xS3)486,155
(C3×C9).33(C3×S3) = C92⋊5C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).33(C3xS3)486,157
(C3×C9).34(C3×S3) = C92⋊11C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).34(C3xS3)486,158
(C3×C9).35(C3×S3) = C3≀C3.S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C9276+(C3xC9).35(C3xS3)486,175
(C3×C9).36(C3×S3) = He3.D9φ: C3×S3/C3 → C6 ⊆ Aut C3×C9816+(C3xC9).36(C3xS3)486,27
(C3×C9).37(C3×S3) = He3.2D9φ: C3×S3/C3 → C6 ⊆ Aut C3×C9816+(C3xC9).37(C3xS3)486,29
(C3×C9).38(C3×S3) = C9⋊(S3×C9)φ: C3×S3/C3 → C6 ⊆ Aut C3×C954(C3xC9).38(C3xS3)486,138
(C3×C9).39(C3×S3) = C92⋊3S3φ: C3×S3/C3 → C6 ⊆ Aut C3×C9546(C3xC9).39(C3xS3)486,139
(C3×C9).40(C3×S3) = C92⋊10C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).40(C3xS3)486,154
(C3×C9).41(C3×S3) = C92⋊12C6φ: C3×S3/C3 → C6 ⊆ Aut C3×C981(C3xC9).41(C3xS3)486,159
(C3×C9).42(C3×S3) = He3.5D9φ: C3×S3/C3 → C6 ⊆ Aut C3×C9816+(C3xC9).42(C3xS3)486,163
(C3×C9).43(C3×S3) = D9×3- 1+2φ: C3×S3/C3 → C6 ⊆ Aut C3×C9546(C3xC9).43(C3xS3)486,101
(C3×C9).44(C3×S3) = S3×C9⋊C9φ: C3×S3/S3 → C3 ⊆ Aut C3×C9162(C3xC9).44(C3xS3)486,97
(C3×C9).45(C3×S3) = S3×C3.He3φ: C3×S3/S3 → C3 ⊆ Aut C3×C9546(C3xC9).45(C3xS3)486,124
(C3×C9).46(C3×S3) = S3×C27⋊C3φ: C3×S3/S3 → C3 ⊆ Aut C3×C9546(C3xC9).46(C3xS3)486,114
(C3×C9).47(C3×S3) = D9×C27φ: C3×S3/C32 → C2 ⊆ Aut C3×C9542(C3xC9).47(C3xS3)486,14
(C3×C9).48(C3×S3) = C32⋊C54φ: C3×S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).48(C3xS3)486,16
(C3×C9).49(C3×S3) = C9⋊C54φ: C3×S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).49(C3xS3)486,30
(C3×C9).50(C3×S3) = D9×C3×C9φ: C3×S3/C32 → C2 ⊆ Aut C3×C954(C3xC9).50(C3xS3)486,91
(C3×C9).51(C3×S3) = C3⋊S3×C27φ: C3×S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9).51(C3xS3)486,161
(C3×C9).52(C3×S3) = C9×D27φ: C3×S3/C32 → C2 ⊆ Aut C3×C9542(C3xC9).52(C3xS3)486,13
(C3×C9).53(C3×S3) = C27⋊3C18φ: C3×S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).53(C3xS3)486,15
(C3×C9).54(C3×S3) = C32⋊D27φ: C3×S3/C32 → C2 ⊆ Aut C3×C981(C3xC9).54(C3xS3)486,17
(C3×C9).55(C3×S3) = C32×D27φ: C3×S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9).55(C3xS3)486,111
(C3×C9).56(C3×S3) = C9×C9⋊S3φ: C3×S3/C32 → C2 ⊆ Aut C3×C954(C3xC9).56(C3xS3)486,133
(C3×C9).57(C3×S3) = C3×C9⋊D9φ: C3×S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9).57(C3xS3)486,134
(C3×C9).58(C3×S3) = He3⋊3D9φ: C3×S3/C32 → C2 ⊆ Aut C3×C981(C3xC9).58(C3xS3)486,142
(C3×C9).59(C3×S3) = C92⋊9C6φ: C3×S3/C32 → C2 ⊆ Aut C3×C981(C3xC9).59(C3xS3)486,144
(C3×C9).60(C3×S3) = C3×C27⋊S3φ: C3×S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9).60(C3xS3)486,160
(C3×C9).61(C3×S3) = C33.5D9φ: C3×S3/C32 → C2 ⊆ Aut C3×C981(C3xC9).61(C3xS3)486,162
(C3×C9).62(C3×S3) = S3×C92central extension (φ=1)162(C3xC9).62(C3xS3)486,92
(C3×C9).63(C3×S3) = S3×C3×C27central extension (φ=1)162(C3xC9).63(C3xS3)486,112

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