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Extensions 1→N→G→Q→1 with N=C3×C9 and Q=C3×C6

Direct product G=N×Q with N=C3×C9 and Q=C3×C6
dρLabelID
C33×C18486C3^3xC18486,250

Semidirect products G=N:Q with N=C3×C9 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C3×C9)⋊1(C3×C6) = C34.S3φ: C3×C6/C1 → C3×C6 ⊆ Aut C3×C927(C3xC9):1(C3xC6)486,105
(C3×C9)⋊2(C3×C6) = C9⋊S3⋊C32φ: C3×C6/C1 → C3×C6 ⊆ Aut C3×C92718+(C3xC9):2(C3xC6)486,129
(C3×C9)⋊3(C3×C6) = He3.(C3×S3)φ: C3×C6/C1 → C3×C6 ⊆ Aut C3×C92718+(C3xC9):3(C3xC6)486,131
(C3×C9)⋊4(C3×C6) = 3- 1+4⋊C2φ: C3×C6/C1 → C3×C6 ⊆ Aut C3×C92718+(C3xC9):4(C3xC6)486,238
(C3×C9)⋊5(C3×C6) = C2×C34.C3φ: C3×C6/C2 → C32 ⊆ Aut C3×C954(C3xC9):5(C3xC6)486,197
(C3×C9)⋊6(C3×C6) = C2×He3.C32φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9):6(C3xC6)486,216
(C3×C9)⋊7(C3×C6) = C2×He3⋊C32φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9):7(C3xC6)486,217
(C3×C9)⋊8(C3×C6) = C2×3- 1+4φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9):8(C3xC6)486,255
(C3×C9)⋊9(C3×C6) = C3×C32⋊D9φ: C3×C6/C3 → C6 ⊆ Aut C3×C954(C3xC9):9(C3xC6)486,94
(C3×C9)⋊10(C3×C6) = C3×He3.S3φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9):10(C3xC6)486,119
(C3×C9)⋊11(C3×C6) = C3×He3.2S3φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9):11(C3xC6)486,122
(C3×C9)⋊12(C3×C6) = C32×C9⋊C6φ: C3×C6/C3 → C6 ⊆ Aut C3×C954(C3xC9):12(C3xC6)486,224
(C3×C9)⋊13(C3×C6) = C3×C33.S3φ: C3×C6/C3 → C6 ⊆ Aut C3×C954(C3xC9):13(C3xC6)486,232
(C3×C9)⋊14(C3×C6) = C3×He3.4S3φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9):14(C3xC6)486,234
(C3×C9)⋊15(C3×C6) = C3×S3×3- 1+2φ: C3×C6/C3 → C6 ⊆ Aut C3×C954(C3xC9):15(C3xC6)486,225
(C3×C9)⋊16(C3×C6) = C6×C32⋊C9φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9):16(C3xC6)486,191
(C3×C9)⋊17(C3×C6) = C6×He3.C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9):17(C3xC6)486,211
(C3×C9)⋊18(C3×C6) = C6×He3⋊C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9):18(C3xC6)486,212
(C3×C9)⋊19(C3×C6) = C3×C6×3- 1+2φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9):19(C3xC6)486,252
(C3×C9)⋊20(C3×C6) = C6×C9○He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9):20(C3xC6)486,253
(C3×C9)⋊21(C3×C6) = S3×C32×C9φ: C3×C6/C32 → C2 ⊆ Aut C3×C9162(C3xC9):21(C3xC6)486,221
(C3×C9)⋊22(C3×C6) = D9×C33φ: C3×C6/C32 → C2 ⊆ Aut C3×C9162(C3xC9):22(C3xC6)486,220
(C3×C9)⋊23(C3×C6) = C32×C9⋊S3φ: C3×C6/C32 → C2 ⊆ Aut C3×C954(C3xC9):23(C3xC6)486,227

Non-split extensions G=N.Q with N=C3×C9 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C3×C9).1(C3×C6) = C2×C27⋊C9φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).1(C3xC6)486,82
(C3×C9).2(C3×C6) = C2×C32.He3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).2(C3xC6)486,88
(C3×C9).3(C3×C6) = C2×C32.5He3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).3(C3xC6)486,89
(C3×C9).4(C3×C6) = C2×C32.6He3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).4(C3xC6)486,90
(C3×C9).5(C3×C6) = C2×C9⋊He3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9162(C3xC9).5(C3xC6)486,198
(C3×C9).6(C3×C6) = C2×C9⋊3- 1+2φ: C3×C6/C2 → C32 ⊆ Aut C3×C9162(C3xC9).6(C3xC6)486,200
(C3×C9).7(C3×C6) = C2×C92⋊9C3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9162(C3xC9).7(C3xC6)486,206
(C3×C9).8(C3×C6) = C2×C32.C33φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).8(C3xC6)486,218
(C3×C9).9(C3×C6) = C2×C9.2He3φ: C3×C6/C2 → C32 ⊆ Aut C3×C9549(C3xC9).9(C3xC6)486,219
(C3×C9).10(C3×C6) = C3×C9⋊C18φ: C3×C6/C3 → C6 ⊆ Aut C3×C954(C3xC9).10(C3xC6)486,96
(C3×C9).11(C3×C6) = C9×C9⋊C6φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9).11(C3xC6)486,100
(C3×C9).12(C3×C6) = D9⋊He3φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9).12(C3xC6)486,106
(C3×C9).13(C3×C6) = D9⋊3- 1+2φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9).13(C3xC6)486,108
(C3×C9).14(C3×C6) = C92⋊7C6φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9).14(C3xC6)486,109
(C3×C9).15(C3×C6) = C92⋊8C6φ: C3×C6/C3 → C6 ⊆ Aut C3×C9186(C3xC9).15(C3xC6)486,110
(C3×C9).16(C3×C6) = S3×C9○He3φ: C3×C6/C3 → C6 ⊆ Aut C3×C9546(C3xC9).16(C3xC6)486,226
(C3×C9).17(C3×C6) = C2×C92⋊C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9543(C3xC9).17(C3xC6)486,85
(C3×C9).18(C3×C6) = C2×C92⋊2C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9543(C3xC9).18(C3xC6)486,86
(C3×C9).19(C3×C6) = C2×C92.C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9543(C3xC9).19(C3xC6)486,87
(C3×C9).20(C3×C6) = C6×C9⋊C9φ: C3×C6/C6 → C3 ⊆ Aut C3×C9486(C3xC9).20(C3xC6)486,192
(C3×C9).21(C3×C6) = C2×C92⋊3C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).21(C3xC6)486,193
(C3×C9).22(C3×C6) = C18×He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).22(C3xC6)486,194
(C3×C9).23(C3×C6) = C18×3- 1+2φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).23(C3xC6)486,195
(C3×C9).24(C3×C6) = C2×C32.23C33φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).24(C3xC6)486,199
(C3×C9).25(C3×C6) = C2×C33.31C32φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).25(C3xC6)486,201
(C3×C9).26(C3×C6) = C2×C92⋊7C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).26(C3xC6)486,202
(C3×C9).27(C3×C6) = C2×C92⋊4C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).27(C3xC6)486,203
(C3×C9).28(C3×C6) = C2×C92⋊5C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).28(C3xC6)486,204
(C3×C9).29(C3×C6) = C2×C92⋊8C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).29(C3xC6)486,205
(C3×C9).30(C3×C6) = C6×C3.He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).30(C3xC6)486,213
(C3×C9).31(C3×C6) = C2×C9.He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9543(C3xC9).31(C3xC6)486,214
(C3×C9).32(C3×C6) = C2×C9.4He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9543(C3xC9).32(C3xC6)486,76
(C3×C9).33(C3×C6) = C2×C9.5He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C91623(C3xC9).33(C3xC6)486,79
(C3×C9).34(C3×C6) = C2×C9.6He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C91623(C3xC9).34(C3xC6)486,80
(C3×C9).35(C3×C6) = C6×C27⋊C3φ: C3×C6/C6 → C3 ⊆ Aut C3×C9162(C3xC9).35(C3xC6)486,208
(C3×C9).36(C3×C6) = C2×C27○He3φ: C3×C6/C6 → C3 ⊆ Aut C3×C91623(C3xC9).36(C3xC6)486,209
(C3×C9).37(C3×C6) = S3×C3×C27φ: C3×C6/C32 → C2 ⊆ Aut C3×C9162(C3xC9).37(C3xC6)486,112
(C3×C9).38(C3×C6) = S3×C27⋊C3φ: C3×C6/C32 → C2 ⊆ Aut C3×C9546(C3xC9).38(C3xC6)486,114
(C3×C9).39(C3×C6) = D9×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C3×C954(C3xC9).39(C3xC6)486,91
(C3×C9).40(C3×C6) = D9×He3φ: C3×C6/C32 → C2 ⊆ Aut C3×C9546(C3xC9).40(C3xC6)486,99
(C3×C9).41(C3×C6) = D9×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C3×C9546(C3xC9).41(C3xC6)486,101
(C3×C9).42(C3×C6) = C2×C27⋊2C9central extension (φ=1)486(C3xC9).42(C3xC6)486,71
(C3×C9).43(C3×C6) = C2×C32⋊C27central extension (φ=1)162(C3xC9).43(C3xC6)486,72
(C3×C9).44(C3×C6) = C2×C9⋊C27central extension (φ=1)486(C3xC9).44(C3xC6)486,81

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