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Extensions 1→N→G→Q→1 with N=C2×C3⋊S3 and Q=D6

Direct product G=N×Q with N=C2×C3⋊S3 and Q=D6
dρLabelID
C22×S3×C3⋊S372C2^2xS3xC3:S3432,768

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=D6
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1D6 = C3⋊S3⋊D12φ: D6/C1 → D6 ⊆ Out C2×C3⋊S33612+(C2xC3:S3):1D6432,301
(C2×C3⋊S3)⋊2D6 = C12.86S32φ: D6/C1 → D6 ⊆ Out C2×C3⋊S3366+(C2xC3:S3):2D6432,302
(C2×C3⋊S3)⋊3D6 = C62⋊2D6φ: D6/C1 → D6 ⊆ Out C2×C3⋊S3366(C2xC3:S3):3D6432,324
(C2×C3⋊S3)⋊4D6 = C2×He3⋊2D4φ: D6/C2 → S3 ⊆ Out C2×C3⋊S372(C2xC3:S3):4D6432,320
(C2×C3⋊S3)⋊5D6 = C2×He3⋊3D4φ: D6/C2 → S3 ⊆ Out C2×C3⋊S372(C2xC3:S3):5D6432,322
(C2×C3⋊S3)⋊6D6 = C62⋊D6φ: D6/C2 → S3 ⊆ Out C2×C3⋊S33612+(C2xC3:S3):6D6432,323
(C2×C3⋊S3)⋊7D6 = C22×C32⋊D6φ: D6/C2 → S3 ⊆ Out C2×C3⋊S336(C2xC3:S3):7D6432,545
(C2×C3⋊S3)⋊8D6 = S3×D6⋊S3φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3):8D6432,597
(C2×C3⋊S3)⋊9D6 = D6⋊S32φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3):9D6432,600
(C2×C3⋊S3)⋊10D6 = C3⋊S3⋊4D12φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):10D6432,602
(C2×C3⋊S3)⋊11D6 = C12⋊3S32φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3):11D6432,691
(C2×C3⋊S3)⋊12D6 = S3×C3⋊D12φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):12D6432,598
(C2×C3⋊S3)⋊13D6 = (S3×C6)⋊D6φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):13D6432,601
(C2×C3⋊S3)⋊14D6 = S3×C12⋊S3φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):14D6432,671
(C2×C3⋊S3)⋊15D6 = C12⋊S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):15D6432,673
(C2×C3⋊S3)⋊16D6 = S3×C32⋊7D4φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):16D6432,684
(C2×C3⋊S3)⋊17D6 = C62⋊23D6φ: D6/S3 → C2 ⊆ Out C2×C3⋊S336(C2xC3:S3):17D6432,686
(C2×C3⋊S3)⋊18D6 = C2×S33φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):18D6432,759
(C2×C3⋊S3)⋊19D6 = C2×C33⋊6D4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):19D6432,680
(C2×C3⋊S3)⋊20D6 = C2×C33⋊8D4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):20D6432,682
(C2×C3⋊S3)⋊21D6 = C3⋊S3×C3⋊D4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):21D6432,685
(C2×C3⋊S3)⋊22D6 = C2×C33⋊9D4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):22D6432,694
(C2×C3⋊S3)⋊23D6 = C62⋊24D6φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3):23D6432,696
(C2×C3⋊S3)⋊24D6 = C22×C32⋊4D6φ: D6/C6 → C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):24D6432,769

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=D6
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).1D6 = C12⋊S3⋊S3φ: D6/C1 → D6 ⊆ Out C2×C3⋊S37212+(C2xC3:S3).1D6432,295
(C2×C3⋊S3).2D6 = C12.84S32φ: D6/C1 → D6 ⊆ Out C2×C3⋊S3726(C2xC3:S3).2D6432,296
(C2×C3⋊S3).3D6 = C62.8D6φ: D6/C1 → D6 ⊆ Out C2×C3⋊S37212-(C2xC3:S3).3D6432,318
(C2×C3⋊S3).4D6 = C62.9D6φ: D6/C1 → D6 ⊆ Out C2×C3⋊S3726(C2xC3:S3).4D6432,319
(C2×C3⋊S3).5D6 = C3⋊S3⋊Dic6φ: D6/C2 → S3 ⊆ Out C2×C3⋊S37212-(C2xC3:S3).5D6432,294
(C2×C3⋊S3).6D6 = C12.91S32φ: D6/C2 → S3 ⊆ Out C2×C3⋊S3726(C2xC3:S3).6D6432,297
(C2×C3⋊S3).7D6 = C12.S32φ: D6/C2 → S3 ⊆ Out C2×C3⋊S37212-(C2xC3:S3).7D6432,299
(C2×C3⋊S3).8D6 = C4×C32⋊D6φ: D6/C2 → S3 ⊆ Out C2×C3⋊S3366(C2xC3:S3).8D6432,300
(C2×C3⋊S3).9D6 = C2×C6.S32φ: D6/C2 → S3 ⊆ Out C2×C3⋊S372(C2xC3:S3).9D6432,317
(C2×C3⋊S3).10D6 = C3⋊S3.2D12φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).10D6432,579
(C2×C3⋊S3).11D6 = S32⋊Dic3φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).11D6432,580
(C2×C3⋊S3).12D6 = C33⋊C4⋊C4φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).12D6432,581
(C2×C3⋊S3).13D6 = (C3×C6).8D12φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).13D6432,586
(C2×C3⋊S3).14D6 = (C3×C6).9D12φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).14D6432,587
(C2×C3⋊S3).15D6 = C6.PSU3(𝔽2)φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).15D6432,592
(C2×C3⋊S3).16D6 = C6.2PSU3(𝔽2)φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).16D6432,593
(C2×C3⋊S3).17D6 = D6.4S32φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).17D6432,608
(C2×C3⋊S3).18D6 = D6.3S32φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).18D6432,609
(C2×C3⋊S3).19D6 = Dic3.S32φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).19D6432,612
(C2×C3⋊S3).20D6 = C62.96D6φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).20D6432,693
(C2×C3⋊S3).21D6 = C2×C33⋊D4φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).21D6432,755
(C2×C3⋊S3).22D6 = C2×C32⋊2D12φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).22D6432,756
(C2×C3⋊S3).23D6 = C2×C33⋊Q8φ: D6/C3 → C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).23D6432,758
(C2×C3⋊S3).24D6 = Dic3×C32⋊C4φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).24D6432,567
(C2×C3⋊S3).25D6 = D6⋊(C32⋊C4)φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).25D6432,568
(C2×C3⋊S3).26D6 = C33⋊(C4⋊C4)φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).26D6432,569
(C2×C3⋊S3).27D6 = S32×Dic3φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).27D6432,594
(C2×C3⋊S3).28D6 = S3×C6.D6φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).28D6432,595
(C2×C3⋊S3).29D6 = Dic3⋊6S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).29D6432,596
(C2×C3⋊S3).30D6 = D6⋊4S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).30D6432,599
(C2×C3⋊S3).31D6 = C33⋊5(C2×Q8)φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).31D6432,604
(C2×C3⋊S3).32D6 = D6.S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).32D6432,607
(C2×C3⋊S3).33D6 = D6.6S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).33D6432,611
(C2×C3⋊S3).34D6 = C12.39S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).34D6432,664
(C2×C3⋊S3).35D6 = C12.57S32φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).35D6432,668
(C2×C3⋊S3).36D6 = C62.91D6φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).36D6432,676
(C2×C3⋊S3).37D6 = C62.93D6φ: D6/S3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).37D6432,678
(C2×C3⋊S3).38D6 = C2×S3×C32⋊C4φ: D6/S3 → C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).38D6432,753
(C2×C3⋊S3).39D6 = C4×C33⋊C4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).39D6432,637
(C2×C3⋊S3).40D6 = C33⋊9(C4⋊C4)φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).40D6432,638
(C2×C3⋊S3).41D6 = C62⋊11Dic3φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).41D6432,641
(C2×C3⋊S3).42D6 = (C3×D12)⋊S3φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).42D6432,661
(C2×C3⋊S3).43D6 = C12.40S32φ: D6/C6 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).43D6432,665
(C2×C3⋊S3).44D6 = C12.73S32φ: D6/C6 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).44D6432,667
(C2×C3⋊S3).45D6 = C3⋊S3⋊4Dic6φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).45D6432,687
(C2×C3⋊S3).46D6 = C12⋊S3⋊12S3φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).46D6432,688
(C2×C3⋊S3).47D6 = C12.95S32φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).47D6432,689
(C2×C3⋊S3).48D6 = C4×C32⋊4D6φ: D6/C6 → C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).48D6432,690
(C2×C3⋊S3).49D6 = C2×C33⋊9(C2×C4)φ: D6/C6 → C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).49D6432,692
(C2×C3⋊S3).50D6 = C22×C33⋊C4φ: D6/C6 → C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).50D6432,766
(C2×C3⋊S3).51D6 = C3⋊S3×Dic6φ: trivial image144(C2xC3:S3).51D6432,663
(C2×C3⋊S3).52D6 = C4×S3×C3⋊S3φ: trivial image72(C2xC3:S3).52D6432,670
(C2×C3⋊S3).53D6 = C3⋊S3×D12φ: trivial image72(C2xC3:S3).53D6432,672
(C2×C3⋊S3).54D6 = C2×Dic3×C3⋊S3φ: trivial image144(C2xC3:S3).54D6432,677

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