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Extensions 1→N→G→Q→1 with N=M4(2) and Q=D4

Direct product G=N×Q with N=M4(2) and Q=D4
dρLabelID
D4×M4(2)32D4xM4(2)128,1666

Semidirect products G=N:Q with N=M4(2) and Q=D4
extensionφ:Q→Out NdρLabelID
M4(2)⋊1D4 = C42⋊9D4φ: D4/C2 → C22 ⊆ Out M4(2)16M4(2):1D4128,734
M4(2)⋊2D4 = C42⋊10D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2):2D4128,736
M4(2)⋊3D4 = M4(2)⋊D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2):3D4128,738
M4(2)⋊4D4 = M4(2)⋊4D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2):4D4128,739
M4(2)⋊5D4 = M4(2)⋊5D4φ: D4/C2 → C22 ⊆ Out M4(2)168+M4(2):5D4128,740
M4(2)⋊6D4 = M4(2)⋊6D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2):6D4128,769
M4(2)⋊7D4 = M4(2)⋊7D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):7D4128,1883
M4(2)⋊8D4 = M4(2)⋊8D4φ: D4/C4 → C2 ⊆ Out M4(2)64M4(2):8D4128,1884
M4(2)⋊9D4 = M4(2)⋊9D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):9D4128,1885
M4(2)⋊10D4 = M4(2)⋊10D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):10D4128,1886
M4(2)⋊11D4 = M4(2)⋊11D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):11D4128,1887
M4(2)⋊12D4 = M4(2)⋊12D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):12D4128,697
M4(2)⋊13D4 = M4(2)⋊13D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2):13D4128,712
M4(2)⋊14D4 = M4(2)⋊14D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2):14D4128,1787
M4(2)⋊15D4 = M4(2)⋊15D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2):15D4128,1788
M4(2)⋊16D4 = M4(2)⋊16D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2):16D4128,1794
M4(2)⋊17D4 = M4(2)⋊17D4φ: D4/C22 → C2 ⊆ Out M4(2)64M4(2):17D4128,1795
M4(2)⋊18D4 = C24.72D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2):18D4128,603
M4(2)⋊19D4 = M4(2)⋊19D4φ: D4/C22 → C2 ⊆ Out M4(2)164M4(2):19D4128,616
M4(2)⋊20D4 = M4(2)⋊20D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2):20D4128,632
M4(2)⋊21D4 = M4(2)⋊21D4φ: D4/C22 → C2 ⊆ Out M4(2)168+M4(2):21D4128,646
M4(2)⋊22D4 = M4(2)⋊22D4φ: trivial image32M4(2):22D4128,1665
M4(2)⋊23D4 = M4(2)⋊23D4φ: trivial image64M4(2):23D4128,1667

Non-split extensions G=N.Q with N=M4(2) and Q=D4
extensionφ:Q→Out NdρLabelID
M4(2).1D4 = C42.129D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).1D4128,735
M4(2).2D4 = C42.130D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).2D4128,737
M4(2).3D4 = M4(2).D4φ: D4/C2 → C22 ⊆ Out M4(2)328-M4(2).3D4128,741
M4(2).4D4 = M4(2).4D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).4D4128,750
M4(2).5D4 = M4(2).5D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).5D4128,751
M4(2).6D4 = M4(2).6D4φ: D4/C2 → C22 ⊆ Out M4(2)64M4(2).6D4128,752
M4(2).7D4 = M4(2).7D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).7D4128,770
M4(2).8D4 = M4(2).8D4φ: D4/C2 → C22 ⊆ Out M4(2)168+M4(2).8D4128,780
M4(2).9D4 = M4(2).9D4φ: D4/C2 → C22 ⊆ Out M4(2)328-M4(2).9D4128,781
M4(2).10D4 = M4(2).10D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).10D4128,783
M4(2).11D4 = M4(2).11D4φ: D4/C2 → C22 ⊆ Out M4(2)64M4(2).11D4128,784
M4(2).12D4 = M4(2).12D4φ: D4/C2 → C22 ⊆ Out M4(2)32M4(2).12D4128,795
M4(2).13D4 = M4(2).13D4φ: D4/C2 → C22 ⊆ Out M4(2)64M4(2).13D4128,796
M4(2).14D4 = C24.Q8φ: D4/C2 → C22 ⊆ Out M4(2)168+M4(2).14D4128,801
M4(2).15D4 = M4(2).15D4φ: D4/C2 → C22 ⊆ Out M4(2)328-M4(2).15D4128,802
M4(2).16D4 = Q16.10D4φ: D4/C2 → C22 ⊆ Out M4(2)324+M4(2).16D4128,924
M4(2).17D4 = Q16.D4φ: D4/C2 → C22 ⊆ Out M4(2)324M4(2).17D4128,925
M4(2).18D4 = D8.3D4φ: D4/C2 → C22 ⊆ Out M4(2)324M4(2).18D4128,926
M4(2).19D4 = D8.12D4φ: D4/C2 → C22 ⊆ Out M4(2)644-M4(2).19D4128,927
M4(2).20D4 = M4(2).20D4φ: D4/C4 → C2 ⊆ Out M4(2)64M4(2).20D4128,1888
M4(2).21D4 = D4○D16φ: D4/C4 → C2 ⊆ Out M4(2)324+M4(2).21D4128,2147
M4(2).22D4 = D4○SD32φ: D4/C4 → C2 ⊆ Out M4(2)324M4(2).22D4128,2148
M4(2).23D4 = Q8○D16φ: D4/C4 → C2 ⊆ Out M4(2)644-M4(2).23D4128,2149
M4(2).24D4 = M4(2).24D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2).24D4128,661
M4(2).25D4 = C42.427D4φ: D4/C4 → C2 ⊆ Out M4(2)164M4(2).25D4128,664
M4(2).26D4 = C42.430D4φ: D4/C4 → C2 ⊆ Out M4(2)64M4(2).26D4128,682
M4(2).27D4 = M4(2).27D4φ: D4/C4 → C2 ⊆ Out M4(2)324M4(2).27D4128,685
M4(2).28D4 = C42.114D4φ: D4/C4 → C2 ⊆ Out M4(2)64M4(2).28D4128,698
M4(2).29D4 = C42.115D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2).29D4128,699
M4(2).30D4 = M4(2).30D4φ: D4/C4 → C2 ⊆ Out M4(2)324M4(2).30D4128,708
M4(2).31D4 = M4(2).31D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2).31D4128,709
M4(2).32D4 = M4(2).32D4φ: D4/C4 → C2 ⊆ Out M4(2)32M4(2).32D4128,710
M4(2).33D4 = M4(2).33D4φ: D4/C4 → C2 ⊆ Out M4(2)64M4(2).33D4128,711
M4(2).34D4 = D4.3D8φ: D4/C4 → C2 ⊆ Out M4(2)324+M4(2).34D4128,953
M4(2).35D4 = D4.4D8φ: D4/C4 → C2 ⊆ Out M4(2)644-M4(2).35D4128,954
M4(2).36D4 = D4.5D8φ: D4/C4 → C2 ⊆ Out M4(2)324M4(2).36D4128,955
M4(2).37D4 = M4(2).37D4φ: D4/C22 → C2 ⊆ Out M4(2)168+M4(2).37D4128,1800
M4(2).38D4 = M4(2).38D4φ: D4/C22 → C2 ⊆ Out M4(2)328-M4(2).38D4128,1801
M4(2).39D4 = C24.10Q8φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2).39D4128,587
M4(2).40D4 = M4(2).40D4φ: D4/C22 → C2 ⊆ Out M4(2)324M4(2).40D4128,590
M4(2).41D4 = M4(2).41D4φ: D4/C22 → C2 ⊆ Out M4(2)164M4(2).41D4128,593
M4(2).42D4 = M4(2).42D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2).42D4128,598
M4(2).43D4 = M4(2).43D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2).43D4128,608
M4(2).44D4 = M4(2).44D4φ: D4/C22 → C2 ⊆ Out M4(2)324M4(2).44D4128,613
M4(2).45D4 = M4(2).45D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2).45D4128,633
M4(2).46D4 = M4(2).46D4φ: D4/C22 → C2 ⊆ Out M4(2)328-M4(2).46D4128,634
M4(2).47D4 = M4(2).47D4φ: D4/C22 → C2 ⊆ Out M4(2)168+M4(2).47D4128,635
M4(2).48D4 = M4(2).48D4φ: D4/C22 → C2 ⊆ Out M4(2)32M4(2).48D4128,639
M4(2).49D4 = M4(2).49D4φ: D4/C22 → C2 ⊆ Out M4(2)64M4(2).49D4128,640
M4(2).50D4 = M4(2).50D4φ: D4/C22 → C2 ⊆ Out M4(2)328-M4(2).50D4128,647
M4(2).51D4 = M4(2).51D4φ: trivial image164M4(2).51D4128,1688
M4(2).52D4 = M4(2)○D8φ: trivial image324M4(2).52D4128,1689

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