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Extensions 1→N→G→Q→1 with N=C2×C4≀C2 and Q=C2

Direct product G=N×Q with N=C2×C4≀C2 and Q=C2
dρLabelID
C22×C4≀C232C2^2xC4wrC2128,1631

Semidirect products G=N:Q with N=C2×C4≀C2 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4≀C2)⋊1C2 = M4(2)⋊D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):1C2128,738
(C2×C4≀C2)⋊2C2 = M4(2)⋊4D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):2C2128,739
(C2×C4≀C2)⋊3C2 = M4(2)⋊6D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):3C2128,769
(C2×C4≀C2)⋊4C2 = C2×D4⋊4D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C216(C2xC4wrC2):4C2128,1746
(C2×C4≀C2)⋊5C2 = C2×D4.9D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):5C2128,1747
(C2×C4≀C2)⋊6C2 = C2×D4.8D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):6C2128,1748
(C2×C4≀C2)⋊7C2 = C2×D4.10D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):7C2128,1749
(C2×C4≀C2)⋊8C2 = C42.313C23φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2):8C2128,1750
(C2×C4≀C2)⋊9C2 = C24.66D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):9C2128,521
(C2×C4≀C2)⋊10C2 = 2+ 1+4⋊3C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):10C2128,524
(C2×C4≀C2)⋊11C2 = 2- 1+4⋊2C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):11C2128,525
(C2×C4≀C2)⋊12C2 = C24.72D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):12C2128,603
(C2×C4≀C2)⋊13C2 = M4(2).43D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):13C2128,608
(C2×C4≀C2)⋊14C2 = C8⋊C22⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):14C2128,615
(C2×C4≀C2)⋊15C2 = (C2×C4)≀C2φ: C2/C1 → C2 ⊆ Out C2×C4≀C216(C2xC4wrC2):15C2128,628
(C2×C4≀C2)⋊16C2 = C42⋊7D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):16C2128,629
(C2×C4≀C2)⋊17C2 = C42.426D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2):17C2128,638
(C2×C4≀C2)⋊18C2 = C43⋊C2φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):18C2128,694
(C2×C4≀C2)⋊19C2 = C42⋊8D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):19C2128,695
(C2×C4≀C2)⋊20C2 = C42.326D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):20C2128,706
(C2×C4≀C2)⋊21C2 = C42.116D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):21C2128,707
(C2×C4≀C2)⋊22C2 = M4(2)⋊13D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):22C2128,712
(C2×C4≀C2)⋊23C2 = C42⋊9D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C216(C2xC4wrC2):23C2128,734
(C2×C4≀C2)⋊24C2 = C42.129D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):24C2128,735
(C2×C4≀C2)⋊25C2 = C42⋊10D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):25C2128,736
(C2×C4≀C2)⋊26C2 = C42⋊11D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):26C2128,771
(C2×C4≀C2)⋊27C2 = C42⋊12D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):27C2128,772
(C2×C4≀C2)⋊28C2 = C42.131D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2):28C2128,782
(C2×C4≀C2)⋊29C2 = C2×C42⋊C22φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):29C2128,1632
(C2×C4≀C2)⋊30C2 = 2- 1+4⋊5C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2):30C2128,1633
(C2×C4≀C2)⋊31C2 = C2×C8.26D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2):31C2128,1686
(C2×C4≀C2)⋊32C2 = M4(2).51D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2):32C2128,1688
(C2×C4≀C2)⋊33C2 = C2×C8○D8φ: trivial image32(C2xC4wrC2):33C2128,1685

Non-split extensions G=N.Q with N=C2×C4≀C2 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4≀C2).1C2 = C4≀C2⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).1C2128,591
(C2×C4≀C2).2C2 = C42⋊9(C2×C4)φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).2C2128,592
(C2×C4≀C2).3C2 = M4(2).41D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2).3C2128,593
(C2×C4≀C2).4C2 = M4(2).7D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).4C2128,770
(C2×C4≀C2).5C2 = D4.C42φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).5C2128,491
(C2×C4≀C2).6C2 = D4.3C42φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).6C2128,497
(C2×C4≀C2).7C2 = C42.102D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).7C2128,538
(C2×C4≀C2).8C2 = M4(2).42D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).8C2128,598
(C2×C4≀C2).9C2 = C8.C22⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).9C2128,614
(C2×C4≀C2).10C2 = M4(2).24D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).10C2128,661
(C2×C4≀C2).11C2 = C42.427D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2).11C2128,664
(C2×C4≀C2).12C2 = C42.428D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).12C2128,669
(C2×C4≀C2).13C2 = C42.107D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).13C2128,670
(C2×C4≀C2).14C2 = C42.130D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C232(C2xC4wrC2).14C2128,737
(C2×C4≀C2).15C2 = C42.8D4φ: C2/C1 → C2 ⊆ Out C2×C4≀C2164(C2xC4wrC2).15C2128,763
(C2×C4≀C2).16C2 = C4×C4≀C2φ: trivial image32(C2xC4wrC2).16C2128,490
(C2×C4≀C2).17C2 = Q8.C42φ: trivial image32(C2xC4wrC2).17C2128,496

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