# Extensions 1→N→G→Q→1 with N=C22×C12 and Q=S3

Direct product G=N×Q with N=C22×C12 and Q=S3
dρLabelID
S3×C22×C1296S3xC2^2xC12288,989

Semidirect products G=N:Q with N=C22×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C12)⋊1S3 = C12×S4φ: S3/C1S3 ⊆ Aut C22×C12363(C2^2xC12):1S3288,897
(C22×C12)⋊2S3 = C12⋊S4φ: S3/C1S3 ⊆ Aut C22×C12366+(C2^2xC12):2S3288,909
(C22×C12)⋊3S3 = C4×C3⋊S4φ: S3/C1S3 ⊆ Aut C22×C12366(C2^2xC12):3S3288,908
(C22×C12)⋊4S3 = C3×C4⋊S4φ: S3/C1S3 ⊆ Aut C22×C12366(C2^2xC12):4S3288,898
(C22×C12)⋊5S3 = C6×D6⋊C4φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12):5S3288,698
(C22×C12)⋊6S3 = C12×C3⋊D4φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12):6S3288,699
(C22×C12)⋊7S3 = C3×C23.28D6φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12):7S3288,700
(C22×C12)⋊8S3 = C2×C6.11D12φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):8S3288,784
(C22×C12)⋊9S3 = C62.129D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):9S3288,786
(C22×C12)⋊10S3 = C6219D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):10S3288,787
(C22×C12)⋊11S3 = C22×C12⋊S3φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):11S3288,1005
(C22×C12)⋊12S3 = C2×C12.59D6φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):12S3288,1006
(C22×C12)⋊13S3 = C4×C327D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):13S3288,785
(C22×C12)⋊14S3 = C22×C4×C3⋊S3φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12):14S3288,1004
(C22×C12)⋊15S3 = C3×C127D4φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12):15S3288,701
(C22×C12)⋊16S3 = C2×C6×D12φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12):16S3288,990
(C22×C12)⋊17S3 = C6×C4○D12φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12):17S3288,991

Non-split extensions G=N.Q with N=C22×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C12).1S3 = C3×A4⋊C8φ: S3/C1S3 ⊆ Aut C22×C12723(C2^2xC12).1S3288,398
(C22×C12).2S3 = C12.1S4φ: S3/C1S3 ⊆ Aut C22×C12726-(C2^2xC12).2S3288,332
(C22×C12).3S3 = C22⋊D36φ: S3/C1S3 ⊆ Aut C22×C12366+(C2^2xC12).3S3288,334
(C22×C12).4S3 = A4⋊Dic6φ: S3/C1S3 ⊆ Aut C22×C12726-(C2^2xC12).4S3288,907
(C22×C12).5S3 = C12.S4φ: S3/C1S3 ⊆ Aut C22×C12726(C2^2xC12).5S3288,68
(C22×C12).6S3 = C4×C3.S4φ: S3/C1S3 ⊆ Aut C22×C12366(C2^2xC12).6S3288,333
(C22×C12).7S3 = C12.12S4φ: S3/C1S3 ⊆ Aut C22×C12726(C2^2xC12).7S3288,402
(C22×C12).8S3 = C3×A4⋊Q8φ: S3/C1S3 ⊆ Aut C22×C12726(C2^2xC12).8S3288,896
(C22×C12).9S3 = C18.C42φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).9S3288,38
(C22×C12).10S3 = C2×Dic9⋊C4φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).10S3288,133
(C22×C12).11S3 = C2×D18⋊C4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).11S3288,137
(C22×C12).12S3 = C23.28D18φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).12S3288,139
(C22×C12).13S3 = C3×C12.55D4φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12).13S3288,264
(C22×C12).14S3 = C3×C6.C42φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12).14S3288,265
(C22×C12).15S3 = C62.15Q8φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).15S3288,306
(C22×C12).16S3 = C6×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12).16S3288,694
(C22×C12).17S3 = C2×C6.Dic6φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).17S3288,780
(C22×C12).18S3 = C36.49D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).18S3288,134
(C22×C12).19S3 = C2×C4⋊Dic9φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).19S3288,135
(C22×C12).20S3 = C367D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).20S3288,140
(C22×C12).21S3 = C22×Dic18φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).21S3288,352
(C22×C12).22S3 = C22×D36φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).22S3288,354
(C22×C12).23S3 = C6210Q8φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).23S3288,781
(C22×C12).24S3 = C2×C12⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).24S3288,782
(C22×C12).25S3 = C22×C324Q8φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).25S3288,1003
(C22×C12).26S3 = C2×C4.Dic9φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).26S3288,131
(C22×C12).27S3 = C23.26D18φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).27S3288,136
(C22×C12).28S3 = C2×D365C2φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).28S3288,355
(C22×C12).29S3 = C2×C12.58D6φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).29S3288,778
(C22×C12).30S3 = C62.247C23φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).30S3288,783
(C22×C12).31S3 = C36.55D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).31S3288,37
(C22×C12).32S3 = C22×C9⋊C8φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).32S3288,130
(C22×C12).33S3 = C2×C4×Dic9φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).33S3288,132
(C22×C12).34S3 = C4×C9⋊D4φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).34S3288,138
(C22×C12).35S3 = C627C8φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).35S3288,305
(C22×C12).36S3 = C22×C4×D9φ: S3/C3C2 ⊆ Aut C22×C12144(C2^2xC12).36S3288,353
(C22×C12).37S3 = C22×C324C8φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).37S3288,777
(C22×C12).38S3 = C2×C4×C3⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C12288(C2^2xC12).38S3288,779
(C22×C12).39S3 = C6×C4.Dic3φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12).39S3288,692
(C22×C12).40S3 = C3×C12.48D4φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12).40S3288,695
(C22×C12).41S3 = C6×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12).41S3288,696
(C22×C12).42S3 = C3×C23.26D6φ: S3/C3C2 ⊆ Aut C22×C1248(C2^2xC12).42S3288,697
(C22×C12).43S3 = C2×C6×Dic6φ: S3/C3C2 ⊆ Aut C22×C1296(C2^2xC12).43S3288,988
(C22×C12).44S3 = C2×C6×C3⋊C8central extension (φ=1)96(C2^2xC12).44S3288,691
(C22×C12).45S3 = Dic3×C2×C12central extension (φ=1)96(C2^2xC12).45S3288,693

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