# Extensions 1→N→G→Q→1 with N=C32×C6 and Q=C2×C4

Direct product G=N×Q with N=C32×C6 and Q=C2×C4
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C32×C6 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C32×C6)⋊(C2×C4) = C2×S3×C32⋊C4φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6248+(C3^2xC6):(C2xC4)432,753
(C32×C6)⋊2(C2×C4) = C2×C6×C32⋊C4φ: C2×C4/C2C4 ⊆ Aut C32×C648(C3^2xC6):2(C2xC4)432,765
(C32×C6)⋊3(C2×C4) = C22×C33⋊C4φ: C2×C4/C2C4 ⊆ Aut C32×C648(C3^2xC6):3(C2xC4)432,766
(C32×C6)⋊4(C2×C4) = S3×C6×Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6):4(C2xC4)432,651
(C32×C6)⋊5(C2×C4) = C6×C6.D6φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6):5(C2xC4)432,654
(C32×C6)⋊6(C2×C4) = C2×S3×C3⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6):6(C2xC4)432,674
(C32×C6)⋊7(C2×C4) = C2×Dic3×C3⋊S3φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6):7(C2xC4)432,677
(C32×C6)⋊8(C2×C4) = C2×C338(C2×C4)φ: C2×C4/C2C22 ⊆ Aut C32×C672(C3^2xC6):8(C2xC4)432,679
(C32×C6)⋊9(C2×C4) = C2×C339(C2×C4)φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6):9(C2xC4)432,692
(C32×C6)⋊10(C2×C4) = S3×C6×C12φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6):10(C2xC4)432,701
(C32×C6)⋊11(C2×C4) = C3⋊S3×C2×C12φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6):11(C2xC4)432,711
(C32×C6)⋊12(C2×C4) = C2×C4×C33⋊C2φ: C2×C4/C4C2 ⊆ Aut C32×C6216(C3^2xC6):12(C2xC4)432,721
(C32×C6)⋊13(C2×C4) = Dic3×C62φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6):13(C2xC4)432,708
(C32×C6)⋊14(C2×C4) = C2×C6×C3⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6):14(C2xC4)432,718
(C32×C6)⋊15(C2×C4) = C22×C335C4φ: C2×C4/C22C2 ⊆ Aut C32×C6432(C3^2xC6):15(C2xC4)432,728

Non-split extensions G=N.Q with N=C32×C6 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C32×C6).1(C2×C4) = Dic3×C32⋊C4φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6488-(C3^2xC6).1(C2xC4)432,567
(C32×C6).2(C2×C4) = D6⋊(C32⋊C4)φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6248+(C3^2xC6).2(C2xC4)432,568
(C32×C6).3(C2×C4) = C33⋊(C4⋊C4)φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6488-(C3^2xC6).3(C2xC4)432,569
(C32×C6).4(C2×C4) = S3×C322C8φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6488-(C3^2xC6).4(C2xC4)432,570
(C32×C6).5(C2×C4) = C335(C2×C8)φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6248+(C3^2xC6).5(C2xC4)432,571
(C32×C6).6(C2×C4) = C33⋊M4(2)φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6488-(C3^2xC6).6(C2xC4)432,572
(C32×C6).7(C2×C4) = C332M4(2)φ: C2×C4/C1C2×C4 ⊆ Aut C32×C6248+(C3^2xC6).7(C2xC4)432,573
(C32×C6).8(C2×C4) = C3×C3⋊S33C8φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).8(C2xC4)432,628
(C32×C6).9(C2×C4) = C3×C32⋊M4(2)φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).9(C2xC4)432,629
(C32×C6).10(C2×C4) = C12×C32⋊C4φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).10(C2xC4)432,630
(C32×C6).11(C2×C4) = C3×C4⋊(C32⋊C4)φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).11(C2xC4)432,631
(C32×C6).12(C2×C4) = C6×C322C8φ: C2×C4/C2C4 ⊆ Aut C32×C648(C3^2xC6).12(C2xC4)432,632
(C32×C6).13(C2×C4) = C3×C62.C4φ: C2×C4/C2C4 ⊆ Aut C32×C6244(C3^2xC6).13(C2xC4)432,633
(C32×C6).14(C2×C4) = C3×C62⋊C4φ: C2×C4/C2C4 ⊆ Aut C32×C6244(C3^2xC6).14(C2xC4)432,634
(C32×C6).15(C2×C4) = C337(C2×C8)φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).15(C2xC4)432,635
(C32×C6).16(C2×C4) = C334M4(2)φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).16(C2xC4)432,636
(C32×C6).17(C2×C4) = C4×C33⋊C4φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).17(C2xC4)432,637
(C32×C6).18(C2×C4) = C339(C4⋊C4)φ: C2×C4/C2C4 ⊆ Aut C32×C6484(C3^2xC6).18(C2xC4)432,638
(C32×C6).19(C2×C4) = C2×C334C8φ: C2×C4/C2C4 ⊆ Aut C32×C648(C3^2xC6).19(C2xC4)432,639
(C32×C6).20(C2×C4) = C3312M4(2)φ: C2×C4/C2C4 ⊆ Aut C32×C6244(C3^2xC6).20(C2xC4)432,640
(C32×C6).21(C2×C4) = C6211Dic3φ: C2×C4/C2C4 ⊆ Aut C32×C6244(C3^2xC6).21(C2xC4)432,641
(C32×C6).22(C2×C4) = C3×S3×C3⋊C8φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).22(C2xC4)432,414
(C32×C6).23(C2×C4) = C3×C12.29D6φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).23(C2xC4)432,415
(C32×C6).24(C2×C4) = C3×D6.Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).24(C2xC4)432,416
(C32×C6).25(C2×C4) = C3×C12.31D6φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).25(C2xC4)432,417
(C32×C6).26(C2×C4) = C3×Dic32φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).26(C2xC4)432,425
(C32×C6).27(C2×C4) = C3×D6⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).27(C2xC4)432,426
(C32×C6).28(C2×C4) = C3×C6.D12φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).28(C2xC4)432,427
(C32×C6).29(C2×C4) = C3×Dic3⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).29(C2xC4)432,428
(C32×C6).30(C2×C4) = C3×C62.C22φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).30(C2xC4)432,429
(C32×C6).31(C2×C4) = S3×C324C8φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).31(C2xC4)432,430
(C32×C6).32(C2×C4) = C3⋊S3×C3⋊C8φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).32(C2xC4)432,431
(C32×C6).33(C2×C4) = C12.69S32φ: C2×C4/C2C22 ⊆ Aut C32×C672(C3^2xC6).33(C2xC4)432,432
(C32×C6).34(C2×C4) = C337M4(2)φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).34(C2xC4)432,433
(C32×C6).35(C2×C4) = C338M4(2)φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).35(C2xC4)432,434
(C32×C6).36(C2×C4) = C339M4(2)φ: C2×C4/C2C22 ⊆ Aut C32×C672(C3^2xC6).36(C2xC4)432,435
(C32×C6).37(C2×C4) = Dic3×C3⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).37(C2xC4)432,448
(C32×C6).38(C2×C4) = C62.77D6φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).38(C2xC4)432,449
(C32×C6).39(C2×C4) = C62.78D6φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).39(C2xC4)432,450
(C32×C6).40(C2×C4) = C62.79D6φ: C2×C4/C2C22 ⊆ Aut C32×C672(C3^2xC6).40(C2xC4)432,451
(C32×C6).41(C2×C4) = C62.80D6φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).41(C2xC4)432,452
(C32×C6).42(C2×C4) = C62.81D6φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).42(C2xC4)432,453
(C32×C6).43(C2×C4) = C62.82D6φ: C2×C4/C2C22 ⊆ Aut C32×C6144(C3^2xC6).43(C2xC4)432,454
(C32×C6).44(C2×C4) = C12.93S32φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).44(C2xC4)432,455
(C32×C6).45(C2×C4) = C3310M4(2)φ: C2×C4/C2C22 ⊆ Aut C32×C6484(C3^2xC6).45(C2xC4)432,456
(C32×C6).46(C2×C4) = C336C42φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).46(C2xC4)432,460
(C32×C6).47(C2×C4) = C62.84D6φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).47(C2xC4)432,461
(C32×C6).48(C2×C4) = C62.85D6φ: C2×C4/C2C22 ⊆ Aut C32×C648(C3^2xC6).48(C2xC4)432,462
(C32×C6).49(C2×C4) = S3×C3×C24φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).49(C2xC4)432,464
(C32×C6).50(C2×C4) = C32×C8⋊S3φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).50(C2xC4)432,465
(C32×C6).51(C2×C4) = Dic3×C3×C12φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).51(C2xC4)432,471
(C32×C6).52(C2×C4) = C32×Dic3⋊C4φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).52(C2xC4)432,472
(C32×C6).53(C2×C4) = C32×D6⋊C4φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).53(C2xC4)432,474
(C32×C6).54(C2×C4) = C3⋊S3×C24φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).54(C2xC4)432,480
(C32×C6).55(C2×C4) = C3×C24⋊S3φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).55(C2xC4)432,481
(C32×C6).56(C2×C4) = C12×C3⋊Dic3φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).56(C2xC4)432,487
(C32×C6).57(C2×C4) = C3×C6.Dic6φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).57(C2xC4)432,488
(C32×C6).58(C2×C4) = C3×C6.11D12φ: C2×C4/C4C2 ⊆ Aut C32×C6144(C3^2xC6).58(C2xC4)432,490
(C32×C6).59(C2×C4) = C8×C33⋊C2φ: C2×C4/C4C2 ⊆ Aut C32×C6216(C3^2xC6).59(C2xC4)432,496
(C32×C6).60(C2×C4) = C3315M4(2)φ: C2×C4/C4C2 ⊆ Aut C32×C6216(C3^2xC6).60(C2xC4)432,497
(C32×C6).61(C2×C4) = C4×C335C4φ: C2×C4/C4C2 ⊆ Aut C32×C6432(C3^2xC6).61(C2xC4)432,503
(C32×C6).62(C2×C4) = C62.146D6φ: C2×C4/C4C2 ⊆ Aut C32×C6432(C3^2xC6).62(C2xC4)432,504
(C32×C6).63(C2×C4) = C62.148D6φ: C2×C4/C4C2 ⊆ Aut C32×C6216(C3^2xC6).63(C2xC4)432,506
(C32×C6).64(C2×C4) = C3×C6×C3⋊C8φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6).64(C2xC4)432,469
(C32×C6).65(C2×C4) = C32×C4.Dic3φ: C2×C4/C22C2 ⊆ Aut C32×C672(C3^2xC6).65(C2xC4)432,470
(C32×C6).66(C2×C4) = C32×C4⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6).66(C2xC4)432,473
(C32×C6).67(C2×C4) = C32×C6.D4φ: C2×C4/C22C2 ⊆ Aut C32×C672(C3^2xC6).67(C2xC4)432,479
(C32×C6).68(C2×C4) = C6×C324C8φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6).68(C2xC4)432,485
(C32×C6).69(C2×C4) = C3×C12.58D6φ: C2×C4/C22C2 ⊆ Aut C32×C672(C3^2xC6).69(C2xC4)432,486
(C32×C6).70(C2×C4) = C3×C12⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C32×C6144(C3^2xC6).70(C2xC4)432,489
(C32×C6).71(C2×C4) = C3×C625C4φ: C2×C4/C22C2 ⊆ Aut C32×C672(C3^2xC6).71(C2xC4)432,495
(C32×C6).72(C2×C4) = C2×C337C8φ: C2×C4/C22C2 ⊆ Aut C32×C6432(C3^2xC6).72(C2xC4)432,501
(C32×C6).73(C2×C4) = C3318M4(2)φ: C2×C4/C22C2 ⊆ Aut C32×C6216(C3^2xC6).73(C2xC4)432,502
(C32×C6).74(C2×C4) = C62.147D6φ: C2×C4/C22C2 ⊆ Aut C32×C6432(C3^2xC6).74(C2xC4)432,505
(C32×C6).75(C2×C4) = C63.C2φ: C2×C4/C22C2 ⊆ Aut C32×C6216(C3^2xC6).75(C2xC4)432,511
(C32×C6).76(C2×C4) = C22⋊C4×C33central extension (φ=1)216(C3^2xC6).76(C2xC4)432,513
(C32×C6).77(C2×C4) = C4⋊C4×C33central extension (φ=1)432(C3^2xC6).77(C2xC4)432,514
(C32×C6).78(C2×C4) = M4(2)×C33central extension (φ=1)216(C3^2xC6).78(C2xC4)432,516

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