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

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

Semidirect products G=N:Q with N=C3×C12 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C3×C12)⋊(C2×C6) = D4×C32⋊C6φ: C2×C6/C1C2×C6 ⊆ Aut C3×C123612+(C3xC12):(C2xC6)432,360
(C3×C12)⋊2(C2×C6) = C2×He34D4φ: C2×C6/C2C6 ⊆ Aut C3×C1272(C3xC12):2(C2xC6)432,350
(C3×C12)⋊3(C2×C6) = C2×C4×C32⋊C6φ: C2×C6/C2C6 ⊆ Aut C3×C1272(C3xC12):3(C2xC6)432,349
(C3×C12)⋊4(C2×C6) = C2×D4×He3φ: C2×C6/C2C6 ⊆ Aut C3×C1272(C3xC12):4(C2xC6)432,404
(C3×C12)⋊5(C2×C6) = C3×S3×D12φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12):5(C2xC6)432,649
(C3×C12)⋊6(C2×C6) = C3×D6⋊D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12):6(C2xC6)432,650
(C3×C12)⋊7(C2×C6) = S3×D4×C32φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12):7(C2xC6)432,704
(C3×C12)⋊8(C2×C6) = C3×D4×C3⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12):8(C2xC6)432,714
(C3×C12)⋊9(C2×C6) = S32×C12φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12):9(C2xC6)432,648
(C3×C12)⋊10(C2×C6) = C22×C4×He3φ: C2×C6/C22C3 ⊆ Aut C3×C12144(C3xC12):10(C2xC6)432,401
(C3×C12)⋊11(C2×C6) = C6×C12⋊S3φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12):11(C2xC6)432,712
(C3×C12)⋊12(C2×C6) = C3×C6×D12φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12):12(C2xC6)432,702
(C3×C12)⋊13(C2×C6) = S3×C6×C12φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12):13(C2xC6)432,701
(C3×C12)⋊14(C2×C6) = C3⋊S3×C2×C12φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12):14(C2xC6)432,711
(C3×C12)⋊15(C2×C6) = D4×C32×C6φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12):15(C2xC6)432,731

Non-split extensions G=N.Q with N=C3×C12 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C3×C12).1(C2×C6) = He38SD16φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212-(C3xC12).1(C2xC6)432,152
(C3×C12).2(C2×C6) = He36D8φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212+(C3xC12).2(C2xC6)432,153
(C3×C12).3(C2×C6) = He36Q16φ: C2×C6/C1C2×C6 ⊆ Aut C3×C1214412-(C3xC12).3(C2xC6)432,160
(C3×C12).4(C2×C6) = He310SD16φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212+(C3xC12).4(C2xC6)432,161
(C3×C12).5(C2×C6) = C62.13D6φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212-(C3xC12).5(C2xC6)432,361
(C3×C12).6(C2×C6) = Q8×C32⋊C6φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212-(C3xC12).6(C2xC6)432,368
(C3×C12).7(C2×C6) = (Q8×He3)⋊C2φ: C2×C6/C1C2×C6 ⊆ Aut C3×C127212+(C3xC12).7(C2xC6)432,369
(C3×C12).8(C2×C6) = He34Q16φ: C2×C6/C2C6 ⊆ Aut C3×C121446-(C3xC12).8(C2xC6)432,114
(C3×C12).9(C2×C6) = He36SD16φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).9(C2xC6)432,117
(C3×C12).10(C2×C6) = He34D8φ: C2×C6/C2C6 ⊆ Aut C3×C12726+(C3xC12).10(C2xC6)432,118
(C3×C12).11(C2×C6) = C2×He33Q8φ: C2×C6/C2C6 ⊆ Aut C3×C12144(C3xC12).11(C2xC6)432,348
(C3×C12).12(C2×C6) = C62.36D6φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).12(C2xC6)432,351
(C3×C12).13(C2×C6) = C8×C32⋊C6φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).13(C2xC6)432,115
(C3×C12).14(C2×C6) = He35M4(2)φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).14(C2xC6)432,116
(C3×C12).15(C2×C6) = C2×He33C8φ: C2×C6/C2C6 ⊆ Aut C3×C12144(C3xC12).15(C2xC6)432,136
(C3×C12).16(C2×C6) = He37M4(2)φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).16(C2xC6)432,137
(C3×C12).17(C2×C6) = D8×He3φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).17(C2xC6)432,216
(C3×C12).18(C2×C6) = D8×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).18(C2xC6)432,217
(C3×C12).19(C2×C6) = SD16×He3φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).19(C2xC6)432,219
(C3×C12).20(C2×C6) = SD16×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).20(C2xC6)432,220
(C3×C12).21(C2×C6) = Q16×He3φ: C2×C6/C2C6 ⊆ Aut C3×C121446(C3xC12).21(C2xC6)432,222
(C3×C12).22(C2×C6) = Q16×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C121446(C3xC12).22(C2xC6)432,223
(C3×C12).23(C2×C6) = C2×D4×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C1272(C3xC12).23(C2xC6)432,405
(C3×C12).24(C2×C6) = C2×Q8×He3φ: C2×C6/C2C6 ⊆ Aut C3×C12144(C3xC12).24(C2xC6)432,407
(C3×C12).25(C2×C6) = C2×Q8×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C12144(C3xC12).25(C2xC6)432,408
(C3×C12).26(C2×C6) = C4○D4×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C3×C12726(C3xC12).26(C2xC6)432,411
(C3×C12).27(C2×C6) = C9×D4⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C12724(C3xC12).27(C2xC6)432,150
(C3×C12).28(C2×C6) = C9×D4.S3φ: C2×C6/C3C22 ⊆ Aut C3×C12724(C3xC12).28(C2xC6)432,151
(C3×C12).29(C2×C6) = C9×Q82S3φ: C2×C6/C3C22 ⊆ Aut C3×C121444(C3xC12).29(C2xC6)432,158
(C3×C12).30(C2×C6) = C9×C3⋊Q16φ: C2×C6/C3C22 ⊆ Aut C3×C121444(C3xC12).30(C2xC6)432,159
(C3×C12).31(C2×C6) = S3×D4×C9φ: C2×C6/C3C22 ⊆ Aut C3×C12724(C3xC12).31(C2xC6)432,358
(C3×C12).32(C2×C6) = C9×D42S3φ: C2×C6/C3C22 ⊆ Aut C3×C12724(C3xC12).32(C2xC6)432,359
(C3×C12).33(C2×C6) = S3×Q8×C9φ: C2×C6/C3C22 ⊆ Aut C3×C121444(C3xC12).33(C2xC6)432,366
(C3×C12).34(C2×C6) = C9×Q83S3φ: C2×C6/C3C22 ⊆ Aut C3×C121444(C3xC12).34(C2xC6)432,367
(C3×C12).35(C2×C6) = C3×C322D8φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).35(C2xC6)432,418
(C3×C12).36(C2×C6) = C3×C3⋊D24φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).36(C2xC6)432,419
(C3×C12).37(C2×C6) = C3×Dic6⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).37(C2xC6)432,420
(C3×C12).38(C2×C6) = C3×D12.S3φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).38(C2xC6)432,421
(C3×C12).39(C2×C6) = C3×C325SD16φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).39(C2xC6)432,422
(C3×C12).40(C2×C6) = C3×C322Q16φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).40(C2xC6)432,423
(C3×C12).41(C2×C6) = C3×C323Q16φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).41(C2xC6)432,424
(C3×C12).42(C2×C6) = C32×D4⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).42(C2xC6)432,475
(C3×C12).43(C2×C6) = C32×D4.S3φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).43(C2xC6)432,476
(C3×C12).44(C2×C6) = C32×Q82S3φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).44(C2xC6)432,477
(C3×C12).45(C2×C6) = C32×C3⋊Q16φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).45(C2xC6)432,478
(C3×C12).46(C2×C6) = C3×C327D8φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).46(C2xC6)432,491
(C3×C12).47(C2×C6) = C3×C329SD16φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).47(C2xC6)432,492
(C3×C12).48(C2×C6) = C3×C3211SD16φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).48(C2xC6)432,493
(C3×C12).49(C2×C6) = C3×C327Q16φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).49(C2xC6)432,494
(C3×C12).50(C2×C6) = C3×S3×Dic6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).50(C2xC6)432,642
(C3×C12).51(C2×C6) = C3×D125S3φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).51(C2xC6)432,643
(C3×C12).52(C2×C6) = C3×D12⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).52(C2xC6)432,644
(C3×C12).53(C2×C6) = C3×Dic3.D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).53(C2xC6)432,645
(C3×C12).54(C2×C6) = C3×D6.6D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).54(C2xC6)432,647
(C3×C12).55(C2×C6) = C32×D42S3φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).55(C2xC6)432,705
(C3×C12).56(C2×C6) = S3×Q8×C32φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).56(C2xC6)432,706
(C3×C12).57(C2×C6) = C32×Q83S3φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).57(C2xC6)432,707
(C3×C12).58(C2×C6) = C3×C12.D6φ: C2×C6/C3C22 ⊆ Aut C3×C1272(C3xC12).58(C2xC6)432,715
(C3×C12).59(C2×C6) = C3×Q8×C3⋊S3φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).59(C2xC6)432,716
(C3×C12).60(C2×C6) = C3×C12.26D6φ: C2×C6/C3C22 ⊆ Aut C3×C12144(C3xC12).60(C2xC6)432,717
(C3×C12).61(C2×C6) = C3×S3×C3⋊C8φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).61(C2xC6)432,414
(C3×C12).62(C2×C6) = C3×C12.29D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).62(C2xC6)432,415
(C3×C12).63(C2×C6) = C3×D6.Dic3φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).63(C2xC6)432,416
(C3×C12).64(C2×C6) = C3×C12.31D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).64(C2xC6)432,417
(C3×C12).65(C2×C6) = C3×D6.D6φ: C2×C6/C3C22 ⊆ Aut C3×C12484(C3xC12).65(C2xC6)432,646
(C3×C12).66(C2×C6) = C2×C8×He3φ: C2×C6/C22C3 ⊆ Aut C3×C12144(C3xC12).66(C2xC6)432,210
(C3×C12).67(C2×C6) = C2×C8×3- 1+2φ: C2×C6/C22C3 ⊆ Aut C3×C12144(C3xC12).67(C2xC6)432,211
(C3×C12).68(C2×C6) = M4(2)×He3φ: C2×C6/C22C3 ⊆ Aut C3×C12726(C3xC12).68(C2xC6)432,213
(C3×C12).69(C2×C6) = M4(2)×3- 1+2φ: C2×C6/C22C3 ⊆ Aut C3×C12726(C3xC12).69(C2xC6)432,214
(C3×C12).70(C2×C6) = C22×C4×3- 1+2φ: C2×C6/C22C3 ⊆ Aut C3×C12144(C3xC12).70(C2xC6)432,402
(C3×C12).71(C2×C6) = C4○D4×He3φ: C2×C6/C22C3 ⊆ Aut C3×C12726(C3xC12).71(C2xC6)432,410
(C3×C12).72(C2×C6) = C3×C242S3φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).72(C2xC6)432,482
(C3×C12).73(C2×C6) = C3×C325D8φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).73(C2xC6)432,483
(C3×C12).74(C2×C6) = C3×C325Q16φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).74(C2xC6)432,484
(C3×C12).75(C2×C6) = C6×C324Q8φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).75(C2xC6)432,710
(C3×C12).76(C2×C6) = C3×C12.59D6φ: C2×C6/C6C2 ⊆ Aut C3×C1272(C3xC12).76(C2xC6)432,713
(C3×C12).77(C2×C6) = C9×C24⋊C2φ: C2×C6/C6C2 ⊆ Aut C3×C121442(C3xC12).77(C2xC6)432,111
(C3×C12).78(C2×C6) = C9×D24φ: C2×C6/C6C2 ⊆ Aut C3×C121442(C3xC12).78(C2xC6)432,112
(C3×C12).79(C2×C6) = C9×Dic12φ: C2×C6/C6C2 ⊆ Aut C3×C121442(C3xC12).79(C2xC6)432,113
(C3×C12).80(C2×C6) = C18×Dic6φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).80(C2xC6)432,341
(C3×C12).81(C2×C6) = C18×D12φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).81(C2xC6)432,346
(C3×C12).82(C2×C6) = C9×C4○D12φ: C2×C6/C6C2 ⊆ Aut C3×C12722(C3xC12).82(C2xC6)432,347
(C3×C12).83(C2×C6) = C32×C24⋊C2φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).83(C2xC6)432,466
(C3×C12).84(C2×C6) = C32×D24φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).84(C2xC6)432,467
(C3×C12).85(C2×C6) = C32×Dic12φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).85(C2xC6)432,468
(C3×C12).86(C2×C6) = C3×C6×Dic6φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).86(C2xC6)432,700
(C3×C12).87(C2×C6) = S3×C72φ: C2×C6/C6C2 ⊆ Aut C3×C121442(C3xC12).87(C2xC6)432,109
(C3×C12).88(C2×C6) = C9×C8⋊S3φ: C2×C6/C6C2 ⊆ Aut C3×C121442(C3xC12).88(C2xC6)432,110
(C3×C12).89(C2×C6) = C18×C3⋊C8φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).89(C2xC6)432,126
(C3×C12).90(C2×C6) = C9×C4.Dic3φ: C2×C6/C6C2 ⊆ Aut C3×C12722(C3xC12).90(C2xC6)432,127
(C3×C12).91(C2×C6) = S3×C2×C36φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).91(C2xC6)432,345
(C3×C12).92(C2×C6) = S3×C3×C24φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).92(C2xC6)432,464
(C3×C12).93(C2×C6) = C32×C8⋊S3φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).93(C2xC6)432,465
(C3×C12).94(C2×C6) = C3×C6×C3⋊C8φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).94(C2xC6)432,469
(C3×C12).95(C2×C6) = C32×C4.Dic3φ: C2×C6/C6C2 ⊆ Aut C3×C1272(C3xC12).95(C2xC6)432,470
(C3×C12).96(C2×C6) = C3⋊S3×C24φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).96(C2xC6)432,480
(C3×C12).97(C2×C6) = C3×C24⋊S3φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).97(C2xC6)432,481
(C3×C12).98(C2×C6) = C6×C324C8φ: C2×C6/C6C2 ⊆ Aut C3×C12144(C3xC12).98(C2xC6)432,485
(C3×C12).99(C2×C6) = C3×C12.58D6φ: C2×C6/C6C2 ⊆ Aut C3×C1272(C3xC12).99(C2xC6)432,486
(C3×C12).100(C2×C6) = C32×C4○D12φ: C2×C6/C6C2 ⊆ Aut C3×C1272(C3xC12).100(C2xC6)432,703
(C3×C12).101(C2×C6) = D8×C3×C9φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).101(C2xC6)432,215
(C3×C12).102(C2×C6) = SD16×C3×C9φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).102(C2xC6)432,218
(C3×C12).103(C2×C6) = Q16×C3×C9φ: C2×C6/C6C2 ⊆ Aut C3×C12432(C3xC12).103(C2xC6)432,221
(C3×C12).104(C2×C6) = D4×C3×C18φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).104(C2xC6)432,403
(C3×C12).105(C2×C6) = Q8×C3×C18φ: C2×C6/C6C2 ⊆ Aut C3×C12432(C3xC12).105(C2xC6)432,406
(C3×C12).106(C2×C6) = C4○D4×C3×C9φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).106(C2xC6)432,409
(C3×C12).107(C2×C6) = D8×C33φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).107(C2xC6)432,517
(C3×C12).108(C2×C6) = SD16×C33φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).108(C2xC6)432,518
(C3×C12).109(C2×C6) = Q16×C33φ: C2×C6/C6C2 ⊆ Aut C3×C12432(C3xC12).109(C2xC6)432,519
(C3×C12).110(C2×C6) = Q8×C32×C6φ: C2×C6/C6C2 ⊆ Aut C3×C12432(C3xC12).110(C2xC6)432,732
(C3×C12).111(C2×C6) = C4○D4×C33φ: C2×C6/C6C2 ⊆ Aut C3×C12216(C3xC12).111(C2xC6)432,733
(C3×C12).112(C2×C6) = M4(2)×C3×C9central extension (φ=1)216(C3xC12).112(C2xC6)432,212
(C3×C12).113(C2×C6) = M4(2)×C33central extension (φ=1)216(C3xC12).113(C2xC6)432,516

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