# Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C2×C6 and Q=C2×C3⋊S3
dρLabelID
C3⋊S3×C22×C6144C3:S3xC2^2xC6432,773

Semidirect products G=N:Q with N=C2×C6 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C2×C3⋊S3) = S3×C3⋊S4φ: C2×C3⋊S3/C3D6 ⊆ Aut C2×C62412+(C2xC6):(C2xC3:S3)432,747
(C2×C6)⋊2(C2×C3⋊S3) = C6×C3⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2×C6366(C2xC6):2(C2xC3:S3)432,761
(C2×C6)⋊3(C2×C3⋊S3) = C2×C324S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2×C654(C2xC6):3(C2xC3:S3)432,762
(C2×C6)⋊4(C2×C3⋊S3) = S3×C327D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C672(C2xC6):4(C2xC3:S3)432,684
(C2×C6)⋊5(C2×C3⋊S3) = C6223D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C636(C2xC6):5(C2xC3:S3)432,686
(C2×C6)⋊6(C2×C3⋊S3) = D4×C33⋊C2φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C6108(C2xC6):6(C2xC3:S3)432,724
(C2×C6)⋊7(C2×C3⋊S3) = C3×D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6):7(C2xC3:S3)432,714
(C2×C6)⋊8(C2×C3⋊S3) = C3⋊S3×C3⋊D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6):8(C2xC3:S3)432,685
(C2×C6)⋊9(C2×C3⋊S3) = C22×S3×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6):9(C2xC3:S3)432,768
(C2×C6)⋊10(C2×C3⋊S3) = C6×C327D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C672(C2xC6):10(C2xC3:S3)432,719
(C2×C6)⋊11(C2×C3⋊S3) = C2×C3315D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6):11(C2xC3:S3)432,729
(C2×C6)⋊12(C2×C3⋊S3) = C23×C33⋊C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6):12(C2xC3:S3)432,774

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C2×C3⋊S3) = C2×C32⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2×C6183(C2xC6).1(C2xC3:S3)432,538
(C2×C6).2(C2×C3⋊S3) = C2×C9⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2×C6546+(C2xC6).2(C2xC3:S3)432,536
(C2×C6).3(C2×C3⋊S3) = C2×C32.3S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2×C654(C2xC6).3(C2xC3:S3)432,537
(C2×C6).4(C2×C3⋊S3) = D4×C9⋊S3φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C6108(C2xC6).4(C2xC3:S3)432,388
(C2×C6).5(C2×C3⋊S3) = C36.27D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C6216(C2xC6).5(C2xC3:S3)432,389
(C2×C6).6(C2×C3⋊S3) = C62.91D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C672(C2xC6).6(C2xC3:S3)432,676
(C2×C6).7(C2×C3⋊S3) = C62.93D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C672(C2xC6).7(C2xC3:S3)432,678
(C2×C6).8(C2×C3⋊S3) = C62.100D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C6216(C2xC6).8(C2xC3:S3)432,725
(C2×C6).9(C2×C3⋊S3) = D4×He3⋊C2φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6366(C2xC6).9(C2xC3:S3)432,390
(C2×C6).10(C2×C3⋊S3) = C62.16D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6726(C2xC6).10(C2xC3:S3)432,391
(C2×C6).11(C2×C3⋊S3) = C3×C12.D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).11(C2xC3:S3)432,715
(C2×C6).12(C2×C3⋊S3) = Dic3×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).12(C2xC3:S3)432,448
(C2×C6).13(C2×C3⋊S3) = C62.77D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).13(C2xC3:S3)432,449
(C2×C6).14(C2×C3⋊S3) = C62.78D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).14(C2xC3:S3)432,450
(C2×C6).15(C2×C3⋊S3) = C62.79D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).15(C2xC3:S3)432,451
(C2×C6).16(C2×C3⋊S3) = C62.80D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).16(C2xC3:S3)432,452
(C2×C6).17(C2×C3⋊S3) = C62.81D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).17(C2xC3:S3)432,453
(C2×C6).18(C2×C3⋊S3) = C62.82D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).18(C2xC3:S3)432,454
(C2×C6).19(C2×C3⋊S3) = C2×S3×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).19(C2xC3:S3)432,674
(C2×C6).20(C2×C3⋊S3) = C62.90D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).20(C2xC3:S3)432,675
(C2×C6).21(C2×C3⋊S3) = C2×Dic3×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).21(C2xC3:S3)432,677
(C2×C6).22(C2×C3⋊S3) = C2×C338(C2×C4)φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).22(C2xC3:S3)432,679
(C2×C6).23(C2×C3⋊S3) = C2×C336D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).23(C2xC3:S3)432,680
(C2×C6).24(C2×C3⋊S3) = C2×C337D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).24(C2xC3:S3)432,681
(C2×C6).25(C2×C3⋊S3) = C2×C338D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C672(C2xC6).25(C2xC3:S3)432,682
(C2×C6).26(C2×C3⋊S3) = C2×C334Q8φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C6144(C2xC6).26(C2xC3:S3)432,683
(C2×C6).27(C2×C3⋊S3) = C62.47D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6726(C2xC6).27(C2xC3:S3)432,387
(C2×C6).28(C2×C3⋊S3) = C3×C12.59D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C672(C2xC6).28(C2xC3:S3)432,713
(C2×C6).29(C2×C3⋊S3) = C4×C9⋊Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).29(C2xC3:S3)432,180
(C2×C6).30(C2×C3⋊S3) = C6.Dic18φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).30(C2xC3:S3)432,181
(C2×C6).31(C2×C3⋊S3) = C36⋊Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).31(C2xC3:S3)432,182
(C2×C6).32(C2×C3⋊S3) = C6.11D36φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).32(C2xC3:S3)432,183
(C2×C6).33(C2×C3⋊S3) = C62.127D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).33(C2xC3:S3)432,198
(C2×C6).34(C2×C3⋊S3) = C2×C12.D9φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).34(C2xC3:S3)432,380
(C2×C6).35(C2×C3⋊S3) = C2×C4×C9⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).35(C2xC3:S3)432,381
(C2×C6).36(C2×C3⋊S3) = C2×C36⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).36(C2xC3:S3)432,382
(C2×C6).37(C2×C3⋊S3) = C36.70D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).37(C2xC3:S3)432,383
(C2×C6).38(C2×C3⋊S3) = C22×C9⋊Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).38(C2xC3:S3)432,396
(C2×C6).39(C2×C3⋊S3) = C2×C6.D18φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).39(C2xC3:S3)432,397
(C2×C6).40(C2×C3⋊S3) = C4×C335C4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).40(C2xC3:S3)432,503
(C2×C6).41(C2×C3⋊S3) = C62.146D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).41(C2xC3:S3)432,504
(C2×C6).42(C2×C3⋊S3) = C62.147D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).42(C2xC3:S3)432,505
(C2×C6).43(C2×C3⋊S3) = C62.148D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).43(C2xC3:S3)432,506
(C2×C6).44(C2×C3⋊S3) = C63.C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).44(C2xC3:S3)432,511
(C2×C6).45(C2×C3⋊S3) = C23×C9⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).45(C2xC3:S3)432,560
(C2×C6).46(C2×C3⋊S3) = C2×C338Q8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).46(C2xC3:S3)432,720
(C2×C6).47(C2×C3⋊S3) = C2×C4×C33⋊C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).47(C2xC3:S3)432,721
(C2×C6).48(C2×C3⋊S3) = C2×C3312D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).48(C2xC3:S3)432,722
(C2×C6).49(C2×C3⋊S3) = C62.160D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6216(C2xC6).49(C2xC3:S3)432,723
(C2×C6).50(C2×C3⋊S3) = C22×C335C4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C6432(C2xC6).50(C2xC3:S3)432,728
(C2×C6).51(C2×C3⋊S3) = C4×He33C4central extension (φ=1)144(C2xC6).51(C2xC3:S3)432,186
(C2×C6).52(C2×C3⋊S3) = C62.29D6central extension (φ=1)144(C2xC6).52(C2xC3:S3)432,187
(C2×C6).53(C2×C3⋊S3) = C62.30D6central extension (φ=1)144(C2xC6).53(C2xC3:S3)432,188
(C2×C6).54(C2×C3⋊S3) = C62.31D6central extension (φ=1)72(C2xC6).54(C2xC3:S3)432,189
(C2×C6).55(C2×C3⋊S3) = C624Dic3central extension (φ=1)72(C2xC6).55(C2xC3:S3)432,199
(C2×C6).56(C2×C3⋊S3) = C2×He34Q8central extension (φ=1)144(C2xC6).56(C2xC3:S3)432,384
(C2×C6).57(C2×C3⋊S3) = C2×C4×He3⋊C2central extension (φ=1)72(C2xC6).57(C2xC3:S3)432,385
(C2×C6).58(C2×C3⋊S3) = C2×He35D4central extension (φ=1)72(C2xC6).58(C2xC3:S3)432,386
(C2×C6).59(C2×C3⋊S3) = C22×He33C4central extension (φ=1)144(C2xC6).59(C2xC3:S3)432,398
(C2×C6).60(C2×C3⋊S3) = C2×He37D4central extension (φ=1)72(C2xC6).60(C2xC3:S3)432,399
(C2×C6).61(C2×C3⋊S3) = C12×C3⋊Dic3central extension (φ=1)144(C2xC6).61(C2xC3:S3)432,487
(C2×C6).62(C2×C3⋊S3) = C3×C6.Dic6central extension (φ=1)144(C2xC6).62(C2xC3:S3)432,488
(C2×C6).63(C2×C3⋊S3) = C3×C12⋊Dic3central extension (φ=1)144(C2xC6).63(C2xC3:S3)432,489
(C2×C6).64(C2×C3⋊S3) = C3×C6.11D12central extension (φ=1)144(C2xC6).64(C2xC3:S3)432,490
(C2×C6).65(C2×C3⋊S3) = C3×C625C4central extension (φ=1)72(C2xC6).65(C2xC3:S3)432,495
(C2×C6).66(C2×C3⋊S3) = C23×He3⋊C2central extension (φ=1)72(C2xC6).66(C2xC3:S3)432,561
(C2×C6).67(C2×C3⋊S3) = C6×C324Q8central extension (φ=1)144(C2xC6).67(C2xC3:S3)432,710
(C2×C6).68(C2×C3⋊S3) = C3⋊S3×C2×C12central extension (φ=1)144(C2xC6).68(C2xC3:S3)432,711
(C2×C6).69(C2×C3⋊S3) = C6×C12⋊S3central extension (φ=1)144(C2xC6).69(C2xC3:S3)432,712
(C2×C6).70(C2×C3⋊S3) = C2×C6×C3⋊Dic3central extension (φ=1)144(C2xC6).70(C2xC3:S3)432,718

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