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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=S3×C6

Direct product G=N×Q with N=C2×C6 and Q=S3×C6
dρLabelID
S3×C2×C62144S3xC2xC6^2432,772

Semidirect products G=N:Q with N=C2×C6 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(S3×C6) = C3×S3×S4φ: S3×C6/C3 → D6 ⊆ Aut C2×C6246(C2xC6):(S3xC6)432,745
(C2×C6)⋊2(S3×C6) = S32×A4φ: S3×C6/S3 → C6 ⊆ Aut C2×C62412+(C2xC6):2(S3xC6)432,749
(C2×C6)⋊3(S3×C6) = C3×C6×S4φ: S3×C6/C6 → S3 ⊆ Aut C2×C654(C2xC6):3(S3xC6)432,760
(C2×C6)⋊4(S3×C6) = C6×C3⋊S4φ: S3×C6/C6 → S3 ⊆ Aut C2×C6366(C2xC6):4(S3xC6)432,761
(C2×C6)⋊5(S3×C6) = C2×A4×C3⋊S3φ: S3×C6/C6 → C6 ⊆ Aut C2×C654(C2xC6):5(S3xC6)432,764
(C2×C6)⋊6(S3×C6) = C3×Dic3⋊D6φ: S3×C6/C32 → C22 ⊆ Aut C2×C6244(C2xC6):6(S3xC6)432,659
(C2×C6)⋊7(S3×C6) = C3×D4×C3⋊S3φ: S3×C6/C32 → C22 ⊆ Aut C2×C672(C2xC6):7(S3xC6)432,714
(C2×C6)⋊8(S3×C6) = S3×C6×A4φ: S3×C6/D6 → C3 ⊆ Aut C2×C6366(C2xC6):8(S3xC6)432,763
(C2×C6)⋊9(S3×C6) = S3×D4×C32φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C672(C2xC6):9(S3xC6)432,704
(C2×C6)⋊10(S3×C6) = C3×S3×C3⋊D4φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C6244(C2xC6):10(S3xC6)432,658
(C2×C6)⋊11(S3×C6) = S32×C2×C6φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6):11(S3xC6)432,767
(C2×C6)⋊12(S3×C6) = C3×C6×C3⋊D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6):12(S3xC6)432,709
(C2×C6)⋊13(S3×C6) = C6×C32⋊7D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6):13(S3xC6)432,719
(C2×C6)⋊14(S3×C6) = C3⋊S3×C22×C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6):14(S3xC6)432,773

Non-split extensions G=N.Q with N=C2×C6 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(S3×C6) = C18×S4φ: S3×C6/C6 → S3 ⊆ Aut C2×C6543(C2xC6).1(S3xC6)432,532
(C2×C6).2(S3×C6) = C2×C32.S4φ: S3×C6/C6 → S3 ⊆ Aut C2×C6186+(C2xC6).2(S3xC6)432,533
(C2×C6).3(S3×C6) = C6×C3.S4φ: S3×C6/C6 → S3 ⊆ Aut C2×C6366(C2xC6).3(S3xC6)432,534
(C2×C6).4(S3×C6) = C2×C62⋊S3φ: S3×C6/C6 → S3 ⊆ Aut C2×C6186+(C2xC6).4(S3xC6)432,535
(C2×C6).5(S3×C6) = C2×D9⋊A4φ: S3×C6/C6 → C6 ⊆ Aut C2×C6546+(C2xC6).5(S3xC6)432,539
(C2×C6).6(S3×C6) = C2×A4×D9φ: S3×C6/C6 → C6 ⊆ Aut C2×C6546+(C2xC6).6(S3xC6)432,540
(C2×C6).7(S3×C6) = C2×C62⋊C6φ: S3×C6/C6 → C6 ⊆ Aut C2×C6186+(C2xC6).7(S3xC6)432,542
(C2×C6).8(S3×C6) = C3×D4×D9φ: S3×C6/C32 → C22 ⊆ Aut C2×C6724(C2xC6).8(S3xC6)432,356
(C2×C6).9(S3×C6) = C3×D4⋊2D9φ: S3×C6/C32 → C22 ⊆ Aut C2×C6724(C2xC6).9(S3xC6)432,357
(C2×C6).10(S3×C6) = D4×C32⋊C6φ: S3×C6/C32 → C22 ⊆ Aut C2×C63612+(C2xC6).10(S3xC6)432,360
(C2×C6).11(S3×C6) = C62.13D6φ: S3×C6/C32 → C22 ⊆ Aut C2×C67212-(C2xC6).11(S3xC6)432,361
(C2×C6).12(S3×C6) = D4×C9⋊C6φ: S3×C6/C32 → C22 ⊆ Aut C2×C63612+(C2xC6).12(S3xC6)432,362
(C2×C6).13(S3×C6) = Dic18⋊2C6φ: S3×C6/C32 → C22 ⊆ Aut C2×C67212-(C2xC6).13(S3xC6)432,363
(C2×C6).14(S3×C6) = C3×D6.3D6φ: S3×C6/C32 → C22 ⊆ Aut C2×C6244(C2xC6).14(S3xC6)432,652
(C2×C6).15(S3×C6) = C3×D6.4D6φ: S3×C6/C32 → C22 ⊆ Aut C2×C6244(C2xC6).15(S3xC6)432,653
(C2×C6).16(S3×C6) = C3×C12.D6φ: S3×C6/C32 → C22 ⊆ Aut C2×C672(C2xC6).16(S3xC6)432,715
(C2×C6).17(S3×C6) = C2×S3×C3.A4φ: S3×C6/D6 → C3 ⊆ Aut C2×C6366(C2xC6).17(S3xC6)432,541
(C2×C6).18(S3×C6) = S3×D4×C9φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C6724(C2xC6).18(S3xC6)432,358
(C2×C6).19(S3×C6) = C9×D4⋊2S3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C6724(C2xC6).19(S3xC6)432,359
(C2×C6).20(S3×C6) = C32×D4⋊2S3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C672(C2xC6).20(S3xC6)432,705
(C2×C6).21(S3×C6) = C3×Dic32φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).21(S3xC6)432,425
(C2×C6).22(S3×C6) = C3×D6⋊Dic3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).22(S3xC6)432,426
(C2×C6).23(S3×C6) = C3×C6.D12φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).23(S3xC6)432,427
(C2×C6).24(S3×C6) = C3×Dic3⋊Dic3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).24(S3xC6)432,428
(C2×C6).25(S3×C6) = C3×C62.C22φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).25(S3xC6)432,429
(C2×C6).26(S3×C6) = S3×C6×Dic3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).26(S3xC6)432,651
(C2×C6).27(S3×C6) = C6×C6.D6φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).27(S3xC6)432,654
(C2×C6).28(S3×C6) = C6×D6⋊S3φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).28(S3xC6)432,655
(C2×C6).29(S3×C6) = C6×C3⋊D12φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).29(S3xC6)432,656
(C2×C6).30(S3×C6) = C6×C32⋊2Q8φ: S3×C6/C3×S3 → C2 ⊆ Aut C2×C648(C2xC6).30(S3xC6)432,657
(C2×C6).31(S3×C6) = C9×C4○D12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6722(C2xC6).31(S3xC6)432,347
(C2×C6).32(S3×C6) = C18×C3⋊D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).32(S3xC6)432,375
(C2×C6).33(S3×C6) = C32×C4○D12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).33(S3xC6)432,703
(C2×C6).34(S3×C6) = C12×Dic9φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).34(S3xC6)432,128
(C2×C6).35(S3×C6) = C3×Dic9⋊C4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).35(S3xC6)432,129
(C2×C6).36(S3×C6) = C3×C4⋊Dic9φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).36(S3xC6)432,130
(C2×C6).37(S3×C6) = C3×D18⋊C4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).37(S3xC6)432,134
(C2×C6).38(S3×C6) = C4×C32⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).38(S3xC6)432,138
(C2×C6).39(S3×C6) = C62.19D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).39(S3xC6)432,139
(C2×C6).40(S3×C6) = C62.20D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).40(S3xC6)432,140
(C2×C6).41(S3×C6) = C62.21D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).41(S3xC6)432,141
(C2×C6).42(S3×C6) = C4×C9⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).42(S3xC6)432,144
(C2×C6).43(S3×C6) = Dic9⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).43(S3xC6)432,145
(C2×C6).44(S3×C6) = C36⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).44(S3xC6)432,146
(C2×C6).45(S3×C6) = D18⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).45(S3xC6)432,147
(C2×C6).46(S3×C6) = C3×C18.D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).46(S3xC6)432,164
(C2×C6).47(S3×C6) = C62⋊3C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).47(S3xC6)432,166
(C2×C6).48(S3×C6) = C62.27D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).48(S3xC6)432,167
(C2×C6).49(S3×C6) = C6×Dic18φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).49(S3xC6)432,340
(C2×C6).50(S3×C6) = D9×C2×C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).50(S3xC6)432,342
(C2×C6).51(S3×C6) = C6×D36φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).51(S3xC6)432,343
(C2×C6).52(S3×C6) = C3×D36⋊5C2φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6722(C2xC6).52(S3xC6)432,344
(C2×C6).53(S3×C6) = C2×He3⋊3Q8φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).53(S3xC6)432,348
(C2×C6).54(S3×C6) = C2×C4×C32⋊C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).54(S3xC6)432,349
(C2×C6).55(S3×C6) = C2×He3⋊4D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).55(S3xC6)432,350
(C2×C6).56(S3×C6) = C62.36D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6726(C2xC6).56(S3xC6)432,351
(C2×C6).57(S3×C6) = C2×C36.C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).57(S3xC6)432,352
(C2×C6).58(S3×C6) = C2×C4×C9⋊C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).58(S3xC6)432,353
(C2×C6).59(S3×C6) = C2×D36⋊C3φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).59(S3xC6)432,354
(C2×C6).60(S3×C6) = D36⋊6C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6726(C2xC6).60(S3xC6)432,355
(C2×C6).61(S3×C6) = C2×C6×Dic9φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).61(S3xC6)432,372
(C2×C6).62(S3×C6) = C6×C9⋊D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).62(S3xC6)432,374
(C2×C6).63(S3×C6) = C22×C32⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).63(S3xC6)432,376
(C2×C6).64(S3×C6) = C2×He3⋊6D4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).64(S3xC6)432,377
(C2×C6).65(S3×C6) = C22×C9⋊C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).65(S3xC6)432,378
(C2×C6).66(S3×C6) = C2×Dic9⋊C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).66(S3xC6)432,379
(C2×C6).67(S3×C6) = C12×C3⋊Dic3φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).67(S3xC6)432,487
(C2×C6).68(S3×C6) = C3×C6.Dic6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).68(S3xC6)432,488
(C2×C6).69(S3×C6) = C3×C12⋊Dic3φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).69(S3xC6)432,489
(C2×C6).70(S3×C6) = C3×C6.11D12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).70(S3xC6)432,490
(C2×C6).71(S3×C6) = C3×C62⋊5C4φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).71(S3xC6)432,495
(C2×C6).72(S3×C6) = D9×C22×C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).72(S3xC6)432,556
(C2×C6).73(S3×C6) = C23×C32⋊C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).73(S3xC6)432,558
(C2×C6).74(S3×C6) = C23×C9⋊C6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).74(S3xC6)432,559
(C2×C6).75(S3×C6) = C6×C32⋊4Q8φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).75(S3xC6)432,710
(C2×C6).76(S3×C6) = C3⋊S3×C2×C12φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).76(S3xC6)432,711
(C2×C6).77(S3×C6) = C6×C12⋊S3φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).77(S3xC6)432,712
(C2×C6).78(S3×C6) = C3×C12.59D6φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C672(C2xC6).78(S3xC6)432,713
(C2×C6).79(S3×C6) = C2×C6×C3⋊Dic3φ: S3×C6/C3×C6 → C2 ⊆ Aut C2×C6144(C2xC6).79(S3xC6)432,718
(C2×C6).80(S3×C6) = Dic3×C36central extension (φ=1)144(C2xC6).80(S3xC6)432,131
(C2×C6).81(S3×C6) = C9×Dic3⋊C4central extension (φ=1)144(C2xC6).81(S3xC6)432,132
(C2×C6).82(S3×C6) = C9×C4⋊Dic3central extension (φ=1)144(C2xC6).82(S3xC6)432,133
(C2×C6).83(S3×C6) = C9×D6⋊C4central extension (φ=1)144(C2xC6).83(S3xC6)432,135
(C2×C6).84(S3×C6) = C9×C6.D4central extension (φ=1)72(C2xC6).84(S3xC6)432,165
(C2×C6).85(S3×C6) = C18×Dic6central extension (φ=1)144(C2xC6).85(S3xC6)432,341
(C2×C6).86(S3×C6) = S3×C2×C36central extension (φ=1)144(C2xC6).86(S3xC6)432,345
(C2×C6).87(S3×C6) = C18×D12central extension (φ=1)144(C2xC6).87(S3xC6)432,346
(C2×C6).88(S3×C6) = Dic3×C2×C18central extension (φ=1)144(C2xC6).88(S3xC6)432,373
(C2×C6).89(S3×C6) = Dic3×C3×C12central extension (φ=1)144(C2xC6).89(S3xC6)432,471
(C2×C6).90(S3×C6) = C32×Dic3⋊C4central extension (φ=1)144(C2xC6).90(S3xC6)432,472
(C2×C6).91(S3×C6) = C32×C4⋊Dic3central extension (φ=1)144(C2xC6).91(S3xC6)432,473
(C2×C6).92(S3×C6) = C32×D6⋊C4central extension (φ=1)144(C2xC6).92(S3xC6)432,474
(C2×C6).93(S3×C6) = C32×C6.D4central extension (φ=1)72(C2xC6).93(S3xC6)432,479
(C2×C6).94(S3×C6) = S3×C22×C18central extension (φ=1)144(C2xC6).94(S3xC6)432,557
(C2×C6).95(S3×C6) = C3×C6×Dic6central extension (φ=1)144(C2xC6).95(S3xC6)432,700
(C2×C6).96(S3×C6) = S3×C6×C12central extension (φ=1)144(C2xC6).96(S3xC6)432,701
(C2×C6).97(S3×C6) = C3×C6×D12central extension (φ=1)144(C2xC6).97(S3xC6)432,702
(C2×C6).98(S3×C6) = Dic3×C62central extension (φ=1)144(C2xC6).98(S3xC6)432,708

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