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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C2×C12

Direct product G=N×Q with N=C3×C6 and Q=C2×C12
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C3×C6 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C2×C12) = C2×C4×C32⋊C6φ: C2×C12/C4 → C6 ⊆ Aut C3×C672(C3xC6):1(C2xC12)432,349
(C3×C6)⋊2(C2×C12) = C22×C32⋊C12φ: C2×C12/C22 → C6 ⊆ Aut C3×C6144(C3xC6):2(C2xC12)432,376
(C3×C6)⋊3(C2×C12) = C2×C6×C32⋊C4φ: C2×C12/C6 → C4 ⊆ Aut C3×C648(C3xC6):3(C2xC12)432,765
(C3×C6)⋊4(C2×C12) = S3×C6×Dic3φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6):4(C2xC12)432,651
(C3×C6)⋊5(C2×C12) = C6×C6.D6φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6):5(C2xC12)432,654
(C3×C6)⋊6(C2×C12) = C22×C4×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6):6(C2xC12)432,401
(C3×C6)⋊7(C2×C12) = S3×C6×C12φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6):7(C2xC12)432,701
(C3×C6)⋊8(C2×C12) = C3⋊S3×C2×C12φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6):8(C2xC12)432,711
(C3×C6)⋊9(C2×C12) = Dic3×C62φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6):9(C2xC12)432,708
(C3×C6)⋊10(C2×C12) = C2×C6×C3⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6):10(C2xC12)432,718

Non-split extensions G=N.Q with N=C3×C6 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C2×C12) = C8×C32⋊C6φ: C2×C12/C4 → C6 ⊆ Aut C3×C6726(C3xC6).1(C2xC12)432,115
(C3×C6).2(C2×C12) = He3⋊5M4(2)φ: C2×C12/C4 → C6 ⊆ Aut C3×C6726(C3xC6).2(C2xC12)432,116
(C3×C6).3(C2×C12) = C62.19D6φ: C2×C12/C4 → C6 ⊆ Aut C3×C6144(C3xC6).3(C2xC12)432,139
(C3×C6).4(C2×C12) = C62.21D6φ: C2×C12/C4 → C6 ⊆ Aut C3×C672(C3xC6).4(C2xC12)432,141
(C3×C6).5(C2×C12) = C2×He3⋊3C8φ: C2×C12/C22 → C6 ⊆ Aut C3×C6144(C3xC6).5(C2xC12)432,136
(C3×C6).6(C2×C12) = He3⋊7M4(2)φ: C2×C12/C22 → C6 ⊆ Aut C3×C6726(C3xC6).6(C2xC12)432,137
(C3×C6).7(C2×C12) = C4×C32⋊C12φ: C2×C12/C22 → C6 ⊆ Aut C3×C6144(C3xC6).7(C2xC12)432,138
(C3×C6).8(C2×C12) = C62.20D6φ: C2×C12/C22 → C6 ⊆ Aut C3×C6144(C3xC6).8(C2xC12)432,140
(C3×C6).9(C2×C12) = C62⋊3C12φ: C2×C12/C22 → C6 ⊆ Aut C3×C672(C3xC6).9(C2xC12)432,166
(C3×C6).10(C2×C12) = C3×C3⋊S3⋊3C8φ: C2×C12/C6 → C4 ⊆ Aut C3×C6484(C3xC6).10(C2xC12)432,628
(C3×C6).11(C2×C12) = C3×C32⋊M4(2)φ: C2×C12/C6 → C4 ⊆ Aut C3×C6484(C3xC6).11(C2xC12)432,629
(C3×C6).12(C2×C12) = C12×C32⋊C4φ: C2×C12/C6 → C4 ⊆ Aut C3×C6484(C3xC6).12(C2xC12)432,630
(C3×C6).13(C2×C12) = C3×C4⋊(C32⋊C4)φ: C2×C12/C6 → C4 ⊆ Aut C3×C6484(C3xC6).13(C2xC12)432,631
(C3×C6).14(C2×C12) = C6×C32⋊2C8φ: C2×C12/C6 → C4 ⊆ Aut C3×C648(C3xC6).14(C2xC12)432,632
(C3×C6).15(C2×C12) = C3×C62.C4φ: C2×C12/C6 → C4 ⊆ Aut C3×C6244(C3xC6).15(C2xC12)432,633
(C3×C6).16(C2×C12) = C3×C62⋊C4φ: C2×C12/C6 → C4 ⊆ Aut C3×C6244(C3xC6).16(C2xC12)432,634
(C3×C6).17(C2×C12) = C3×S3×C3⋊C8φ: C2×C12/C6 → C22 ⊆ Aut C3×C6484(C3xC6).17(C2xC12)432,414
(C3×C6).18(C2×C12) = C3×C12.29D6φ: C2×C12/C6 → C22 ⊆ Aut C3×C6484(C3xC6).18(C2xC12)432,415
(C3×C6).19(C2×C12) = C3×D6.Dic3φ: C2×C12/C6 → C22 ⊆ Aut C3×C6484(C3xC6).19(C2xC12)432,416
(C3×C6).20(C2×C12) = C3×C12.31D6φ: C2×C12/C6 → C22 ⊆ Aut C3×C6484(C3xC6).20(C2xC12)432,417
(C3×C6).21(C2×C12) = C3×Dic32φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6).21(C2xC12)432,425
(C3×C6).22(C2×C12) = C3×D6⋊Dic3φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6).22(C2xC12)432,426
(C3×C6).23(C2×C12) = C3×C6.D12φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6).23(C2xC12)432,427
(C3×C6).24(C2×C12) = C3×Dic3⋊Dic3φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6).24(C2xC12)432,428
(C3×C6).25(C2×C12) = C3×C62.C22φ: C2×C12/C6 → C22 ⊆ Aut C3×C648(C3xC6).25(C2xC12)432,429
(C3×C6).26(C2×C12) = C42×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).26(C2xC12)432,201
(C3×C6).27(C2×C12) = C42×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).27(C2xC12)432,202
(C3×C6).28(C2×C12) = C22⋊C4×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C672(C3xC6).28(C2xC12)432,204
(C3×C6).29(C2×C12) = C22⋊C4×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C672(C3xC6).29(C2xC12)432,205
(C3×C6).30(C2×C12) = C4⋊C4×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).30(C2xC12)432,207
(C3×C6).31(C2×C12) = C4⋊C4×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).31(C2xC12)432,208
(C3×C6).32(C2×C12) = C2×C8×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).32(C2xC12)432,210
(C3×C6).33(C2×C12) = C2×C8×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).33(C2xC12)432,211
(C3×C6).34(C2×C12) = M4(2)×He3φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6726(C3xC6).34(C2xC12)432,213
(C3×C6).35(C2×C12) = M4(2)×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6726(C3xC6).35(C2xC12)432,214
(C3×C6).36(C2×C12) = C22×C4×3- 1+2φ: C2×C12/C2×C4 → C3 ⊆ Aut C3×C6144(C3xC6).36(C2xC12)432,402
(C3×C6).37(C2×C12) = S3×C72φ: C2×C12/C12 → C2 ⊆ Aut C3×C61442(C3xC6).37(C2xC12)432,109
(C3×C6).38(C2×C12) = C9×C8⋊S3φ: C2×C12/C12 → C2 ⊆ Aut C3×C61442(C3xC6).38(C2xC12)432,110
(C3×C6).39(C2×C12) = Dic3×C36φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).39(C2xC12)432,131
(C3×C6).40(C2×C12) = C9×Dic3⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).40(C2xC12)432,132
(C3×C6).41(C2×C12) = C9×D6⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).41(C2xC12)432,135
(C3×C6).42(C2×C12) = S3×C2×C36φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).42(C2xC12)432,345
(C3×C6).43(C2×C12) = S3×C3×C24φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).43(C2xC12)432,464
(C3×C6).44(C2×C12) = C32×C8⋊S3φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).44(C2xC12)432,465
(C3×C6).45(C2×C12) = C32×Dic3⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).45(C2xC12)432,472
(C3×C6).46(C2×C12) = C32×D6⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).46(C2xC12)432,474
(C3×C6).47(C2×C12) = C3⋊S3×C24φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).47(C2xC12)432,480
(C3×C6).48(C2×C12) = C3×C24⋊S3φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).48(C2xC12)432,481
(C3×C6).49(C2×C12) = C3×C6.Dic6φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).49(C2xC12)432,488
(C3×C6).50(C2×C12) = C3×C6.11D12φ: C2×C12/C12 → C2 ⊆ Aut C3×C6144(C3xC6).50(C2xC12)432,490
(C3×C6).51(C2×C12) = C18×C3⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).51(C2xC12)432,126
(C3×C6).52(C2×C12) = C9×C4.Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6722(C3xC6).52(C2xC12)432,127
(C3×C6).53(C2×C12) = C9×C4⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).53(C2xC12)432,133
(C3×C6).54(C2×C12) = C9×C6.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).54(C2xC12)432,165
(C3×C6).55(C2×C12) = Dic3×C2×C18φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).55(C2xC12)432,373
(C3×C6).56(C2×C12) = C3×C6×C3⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).56(C2xC12)432,469
(C3×C6).57(C2×C12) = C32×C4.Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).57(C2xC12)432,470
(C3×C6).58(C2×C12) = Dic3×C3×C12φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).58(C2xC12)432,471
(C3×C6).59(C2×C12) = C32×C4⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).59(C2xC12)432,473
(C3×C6).60(C2×C12) = C32×C6.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).60(C2xC12)432,479
(C3×C6).61(C2×C12) = C6×C32⋊4C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).61(C2xC12)432,485
(C3×C6).62(C2×C12) = C3×C12.58D6φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).62(C2xC12)432,486
(C3×C6).63(C2×C12) = C12×C3⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).63(C2xC12)432,487
(C3×C6).64(C2×C12) = C3×C12⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).64(C2xC12)432,489
(C3×C6).65(C2×C12) = C3×C62⋊5C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).65(C2xC12)432,495
(C3×C6).66(C2×C12) = C22⋊C4×C3×C9central extension (φ=1)216(C3xC6).66(C2xC12)432,203
(C3×C6).67(C2×C12) = C4⋊C4×C3×C9central extension (φ=1)432(C3xC6).67(C2xC12)432,206
(C3×C6).68(C2×C12) = M4(2)×C3×C9central extension (φ=1)216(C3xC6).68(C2xC12)432,212
(C3×C6).69(C2×C12) = C22⋊C4×C33central extension (φ=1)216(C3xC6).69(C2xC12)432,513
(C3×C6).70(C2×C12) = C4⋊C4×C33central extension (φ=1)432(C3xC6).70(C2xC12)432,514
(C3×C6).71(C2×C12) = M4(2)×C33central extension (φ=1)216(C3xC6).71(C2xC12)432,516

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