Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C2×C4 and Q=C2×C3⋊S3
dρLabelID
C22×C4×C3⋊S3144C2^2xC4xC3:S3288,1004

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C3⋊S3) = C6212D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4):1(C2xC3:S3)288,739
(C2×C4)⋊2(C2×C3⋊S3) = C6213D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4):2(C2xC3:S3)288,794
(C2×C4)⋊3(C2×C3⋊S3) = C3282+ 1+4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4):3(C2xC3:S3)288,1009
(C2×C4)⋊4(C2×C3⋊S3) = C62.154C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4):4(C2xC3:S3)288,1014
(C2×C4)⋊5(C2×C3⋊S3) = C22⋊C4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4):5(C2xC3:S3)288,737
(C2×C4)⋊6(C2×C3⋊S3) = C2×D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4):6(C2xC3:S3)288,1007
(C2×C4)⋊7(C2×C3⋊S3) = C4○D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4):7(C2xC3:S3)288,1013
(C2×C4)⋊8(C2×C3⋊S3) = C2×C6.11D12φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4):8(C2xC3:S3)288,784
(C2×C4)⋊9(C2×C3⋊S3) = C22×C12⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4):9(C2xC3:S3)288,1005
(C2×C4)⋊10(C2×C3⋊S3) = C2×C12.59D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4):10(C2xC3:S3)288,1006

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C3⋊S3) = C12.19D12φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4).1(C2xC3:S3)288,298
(C2×C4).2(C2×C3⋊S3) = C12.20D12φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).2(C2xC3:S3)288,299
(C2×C4).3(C2×C3⋊S3) = (C6×D4).S3φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4).3(C2xC3:S3)288,308
(C2×C4).4(C2×C3⋊S3) = (C6×C12).C4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).4(C2xC3:S3)288,311
(C2×C4).5(C2×C3⋊S3) = C626Q8φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).5(C2xC3:S3)288,735
(C2×C4).6(C2×C3⋊S3) = C62.228C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).6(C2xC3:S3)288,741
(C2×C4).7(C2×C3⋊S3) = C62.69D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).7(C2xC3:S3)288,743
(C2×C4).8(C2×C3⋊S3) = C122Dic6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4288(C2xC4).8(C2xC3:S3)288,745
(C2×C4).9(C2×C3⋊S3) = C62.233C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4288(C2xC4).9(C2xC3:S3)288,746
(C2×C4).10(C2×C3⋊S3) = C62.234C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4288(C2xC4).10(C2xC3:S3)288,747
(C2×C4).11(C2×C3⋊S3) = C62.238C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).11(C2xC3:S3)288,751
(C2×C4).12(C2×C3⋊S3) = C123D12φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).12(C2xC3:S3)288,752
(C2×C4).13(C2×C3⋊S3) = C62.240C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).13(C2xC3:S3)288,753
(C2×C4).14(C2×C3⋊S3) = C12.31D12φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).14(C2xC3:S3)288,754
(C2×C4).15(C2×C3⋊S3) = C243D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4).15(C2xC3:S3)288,765
(C2×C4).16(C2×C3⋊S3) = C24.5D6φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).16(C2xC3:S3)288,766
(C2×C4).17(C2×C3⋊S3) = C62.131D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4).17(C2xC3:S3)288,789
(C2×C4).18(C2×C3⋊S3) = C62.72D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).18(C2xC3:S3)288,792
(C2×C4).19(C2×C3⋊S3) = C6214D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).19(C2xC3:S3)288,796
(C2×C4).20(C2×C3⋊S3) = C62.134D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).20(C2xC3:S3)288,799
(C2×C4).21(C2×C3⋊S3) = C62.73D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C472(C2xC4).21(C2xC3:S3)288,806
(C2×C4).22(C2×C3⋊S3) = C62.75D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).22(C2xC3:S3)288,808
(C2×C4).23(C2×C3⋊S3) = C3272- 1+4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).23(C2xC3:S3)288,1012
(C2×C4).24(C2×C3⋊S3) = C3292- 1+4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2×C4144(C2xC4).24(C2xC3:S3)288,1015
(C2×C4).25(C2×C3⋊S3) = C62.221C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).25(C2xC3:S3)288,734
(C2×C4).26(C2×C3⋊S3) = C62.223C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).26(C2xC3:S3)288,736
(C2×C4).27(C2×C3⋊S3) = C62.225C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).27(C2xC3:S3)288,738
(C2×C4).28(C2×C3⋊S3) = C62.227C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).28(C2xC3:S3)288,740
(C2×C4).29(C2×C3⋊S3) = C62.229C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).29(C2xC3:S3)288,742
(C2×C4).30(C2×C3⋊S3) = C62.231C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).30(C2xC3:S3)288,744
(C2×C4).31(C2×C3⋊S3) = C4⋊C4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).31(C2xC3:S3)288,748
(C2×C4).32(C2×C3⋊S3) = C62.236C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).32(C2xC3:S3)288,749
(C2×C4).33(C2×C3⋊S3) = C62.242C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).33(C2xC3:S3)288,755
(C2×C4).34(C2×C3⋊S3) = C12.9Dic6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).34(C2xC3:S3)288,282
(C2×C4).35(C2×C3⋊S3) = C12.10Dic6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).35(C2xC3:S3)288,283
(C2×C4).36(C2×C3⋊S3) = C62.113D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).36(C2xC3:S3)288,284
(C2×C4).37(C2×C3⋊S3) = C62.114D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).37(C2xC3:S3)288,285
(C2×C4).38(C2×C3⋊S3) = C62.8Q8φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).38(C2xC3:S3)288,297
(C2×C4).39(C2×C3⋊S3) = C62.37D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4).39(C2xC3:S3)288,300
(C2×C4).40(C2×C3⋊S3) = C62.116D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).40(C2xC3:S3)288,307
(C2×C4).41(C2×C3⋊S3) = C62.117D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).41(C2xC3:S3)288,310
(C2×C4).42(C2×C3⋊S3) = C62.39D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4).42(C2xC3:S3)288,312
(C2×C4).43(C2×C3⋊S3) = C62.237C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).43(C2xC3:S3)288,750
(C2×C4).44(C2×C3⋊S3) = M4(2)×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C472(C2xC4).44(C2xC3:S3)288,763
(C2×C4).45(C2×C3⋊S3) = C24.47D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).45(C2xC3:S3)288,764
(C2×C4).46(C2×C3⋊S3) = C2×C327D8φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).46(C2xC3:S3)288,788
(C2×C4).47(C2×C3⋊S3) = C2×C329SD16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).47(C2xC3:S3)288,790
(C2×C4).48(C2×C3⋊S3) = D4×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).48(C2xC3:S3)288,791
(C2×C4).49(C2×C3⋊S3) = C62.254C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).49(C2xC3:S3)288,793
(C2×C4).50(C2×C3⋊S3) = C62.256C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).50(C2xC3:S3)288,795
(C2×C4).51(C2×C3⋊S3) = C62.258C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).51(C2xC3:S3)288,797
(C2×C4).52(C2×C3⋊S3) = C2×C3211SD16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).52(C2xC3:S3)288,798
(C2×C4).53(C2×C3⋊S3) = C2×C327Q16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).53(C2xC3:S3)288,800
(C2×C4).54(C2×C3⋊S3) = C62.259C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).54(C2xC3:S3)288,801
(C2×C4).55(C2×C3⋊S3) = Q8×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4288(C2xC4).55(C2xC3:S3)288,802
(C2×C4).56(C2×C3⋊S3) = C62.261C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).56(C2xC3:S3)288,803
(C2×C4).57(C2×C3⋊S3) = C62.262C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).57(C2xC3:S3)288,804
(C2×C4).58(C2×C3⋊S3) = D4.(C3⋊Dic3)φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).58(C2xC3:S3)288,805
(C2×C4).59(C2×C3⋊S3) = C62.74D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).59(C2xC3:S3)288,807
(C2×C4).60(C2×C3⋊S3) = C2×C12.D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).60(C2xC3:S3)288,1008
(C2×C4).61(C2×C3⋊S3) = C2×Q8×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).61(C2xC3:S3)288,1010
(C2×C4).62(C2×C3⋊S3) = C2×C12.26D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2×C4144(C2xC4).62(C2xC3:S3)288,1011
(C2×C4).63(C2×C3⋊S3) = C12.25Dic6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).63(C2xC3:S3)288,727
(C2×C4).64(C2×C3⋊S3) = C12216C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).64(C2xC3:S3)288,729
(C2×C4).65(C2×C3⋊S3) = C1226C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).65(C2xC3:S3)288,732
(C2×C4).66(C2×C3⋊S3) = C1222C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).66(C2xC3:S3)288,733
(C2×C4).67(C2×C3⋊S3) = C2×C6.Dic6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).67(C2xC3:S3)288,780
(C2×C4).68(C2×C3⋊S3) = C62.129D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).68(C2xC3:S3)288,786
(C2×C4).69(C2×C3⋊S3) = C6219D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).69(C2xC3:S3)288,787
(C2×C4).70(C2×C3⋊S3) = C122⋊C2φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C472(C2xC4).70(C2xC3:S3)288,280
(C2×C4).71(C2×C3⋊S3) = C6.4Dic12φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).71(C2xC3:S3)288,291
(C2×C4).72(C2×C3⋊S3) = C242Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).72(C2xC3:S3)288,292
(C2×C4).73(C2×C3⋊S3) = C241Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).73(C2xC3:S3)288,293
(C2×C4).74(C2×C3⋊S3) = C12.59D12φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).74(C2xC3:S3)288,294
(C2×C4).75(C2×C3⋊S3) = C62.84D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).75(C2xC3:S3)288,296
(C2×C4).76(C2×C3⋊S3) = C126Dic6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).76(C2xC3:S3)288,726
(C2×C4).77(C2×C3⋊S3) = C124D12φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).77(C2xC3:S3)288,731
(C2×C4).78(C2×C3⋊S3) = C24.95D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).78(C2xC3:S3)288,758
(C2×C4).79(C2×C3⋊S3) = C2×C242S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).79(C2xC3:S3)288,759
(C2×C4).80(C2×C3⋊S3) = C2×C325D8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).80(C2xC3:S3)288,760
(C2×C4).81(C2×C3⋊S3) = C24.78D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).81(C2xC3:S3)288,761
(C2×C4).82(C2×C3⋊S3) = C2×C325Q16φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).82(C2xC3:S3)288,762
(C2×C4).83(C2×C3⋊S3) = C2×C12.58D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).83(C2xC3:S3)288,778
(C2×C4).84(C2×C3⋊S3) = C6210Q8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4144(C2xC4).84(C2xC3:S3)288,781
(C2×C4).85(C2×C3⋊S3) = C2×C12⋊Dic3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).85(C2xC3:S3)288,782
(C2×C4).86(C2×C3⋊S3) = C22×C324Q8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2×C4288(C2xC4).86(C2xC3:S3)288,1003
(C2×C4).87(C2×C3⋊S3) = C4×C324C8central extension (φ=1)288(C2xC4).87(C2xC3:S3)288,277
(C2×C4).88(C2×C3⋊S3) = C122.C2central extension (φ=1)288(C2xC4).88(C2xC3:S3)288,278
(C2×C4).89(C2×C3⋊S3) = C12.57D12central extension (φ=1)288(C2xC4).89(C2xC3:S3)288,279
(C2×C4).90(C2×C3⋊S3) = C8×C3⋊Dic3central extension (φ=1)288(C2xC4).90(C2xC3:S3)288,288
(C2×C4).91(C2×C3⋊S3) = C12.30Dic6central extension (φ=1)288(C2xC4).91(C2xC3:S3)288,289
(C2×C4).92(C2×C3⋊S3) = C24⋊Dic3central extension (φ=1)288(C2xC4).92(C2xC3:S3)288,290
(C2×C4).93(C2×C3⋊S3) = C12.60D12central extension (φ=1)144(C2xC4).93(C2xC3:S3)288,295
(C2×C4).94(C2×C3⋊S3) = C627C8central extension (φ=1)144(C2xC4).94(C2xC3:S3)288,305
(C2×C4).95(C2×C3⋊S3) = C4×C324Q8central extension (φ=1)288(C2xC4).95(C2xC3:S3)288,725
(C2×C4).96(C2×C3⋊S3) = C42×C3⋊S3central extension (φ=1)144(C2xC4).96(C2xC3:S3)288,728
(C2×C4).97(C2×C3⋊S3) = C4×C12⋊S3central extension (φ=1)144(C2xC4).97(C2xC3:S3)288,730
(C2×C4).98(C2×C3⋊S3) = C2×C8×C3⋊S3central extension (φ=1)144(C2xC4).98(C2xC3:S3)288,756
(C2×C4).99(C2×C3⋊S3) = C2×C24⋊S3central extension (φ=1)144(C2xC4).99(C2xC3:S3)288,757
(C2×C4).100(C2×C3⋊S3) = C22×C324C8central extension (φ=1)288(C2xC4).100(C2xC3:S3)288,777
(C2×C4).101(C2×C3⋊S3) = C2×C4×C3⋊Dic3central extension (φ=1)288(C2xC4).101(C2xC3:S3)288,779
(C2×C4).102(C2×C3⋊S3) = C62.247C23central extension (φ=1)144(C2xC4).102(C2xC3:S3)288,783
(C2×C4).103(C2×C3⋊S3) = C4×C327D4central extension (φ=1)144(C2xC4).103(C2xC3:S3)288,785

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