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Extensions 1→N→G→Q→1 with N=C4⋊M4(2) and Q=C2

Direct product G=N×Q with N=C4⋊M4(2) and Q=C2
dρLabelID
C2×C4⋊M4(2)64C2xC4:M4(2)128,1635

Semidirect products G=N:Q with N=C4⋊M4(2) and Q=C2
extensionφ:Q→Out NdρLabelID
C4⋊M4(2)⋊1C2 = C42.131D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)164C4:M4(2):1C2128,782
C4⋊M4(2)⋊2C2 = C42.211D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):2C2128,1768
C4⋊M4(2)⋊3C2 = C42.212D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):3C2128,1769
C4⋊M4(2)⋊4C2 = C42.444D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):4C2128,1770
C4⋊M4(2)⋊5C2 = C42.445D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):5C2128,1771
C4⋊M4(2)⋊6C2 = C42.446D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):6C2128,1772
C4⋊M4(2)⋊7C2 = C42.219D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):7C2128,1809
C4⋊M4(2)⋊8C2 = C42.448D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):8C2128,1811
C4⋊M4(2)⋊9C2 = C42.449D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):9C2128,1812
C4⋊M4(2)⋊10C2 = C42.299D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):10C2128,1983
C4⋊M4(2)⋊11C2 = C42.300D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):11C2128,1984
C4⋊M4(2)⋊12C2 = C42.301D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):12C2128,1985
C4⋊M4(2)⋊13C2 = C42.302D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):13C2128,1986
C4⋊M4(2)⋊14C2 = C42.304D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):14C2128,1988
C4⋊M4(2)⋊15C2 = D4⋊M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):15C2128,218
C4⋊M4(2)⋊16C2 = D4⋊4M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):16C2128,221
C4⋊M4(2)⋊17C2 = C42.315D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):17C2128,224
C4⋊M4(2)⋊18C2 = C42.52D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):18C2128,227
C4⋊M4(2)⋊19C2 = C42.413D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):19C2128,277
C4⋊M4(2)⋊20C2 = C42.78D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):20C2128,279
C4⋊M4(2)⋊21C2 = C42.84D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):21C2128,289
C4⋊M4(2)⋊22C2 = C42.87D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):22C2128,292
C4⋊M4(2)⋊23C2 = C42.96D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):23C2128,532
C4⋊M4(2)⋊24C2 = C42.102D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):24C2128,538
C4⋊M4(2)⋊25C2 = M4(2).41D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)164C4:M4(2):25C2128,593
C4⋊M4(2)⋊26C2 = C43⋊C2φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):26C2128,694
C4⋊M4(2)⋊27C2 = C42⋊8D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):27C2128,695
C4⋊M4(2)⋊28C2 = M4(2)⋊12D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):28C2128,697
C4⋊M4(2)⋊29C2 = C42.115D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):29C2128,699
C4⋊M4(2)⋊30C2 = C42.257C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):30C2128,1637
C4⋊M4(2)⋊31C2 = C42.674C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):31C2128,1638
C4⋊M4(2)⋊32C2 = C42.259C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):32C2128,1653
C4⋊M4(2)⋊33C2 = C42.678C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):33C2128,1657
C4⋊M4(2)⋊34C2 = C42.266C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):34C2128,1664
C4⋊M4(2)⋊35C2 = D4×M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2):35C2128,1666
C4⋊M4(2)⋊36C2 = C42.698C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):36C2128,1721
C4⋊M4(2)⋊37C2 = D4⋊8M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):37C2128,1722
C4⋊M4(2)⋊38C2 = Q8⋊7M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):38C2128,1723
C4⋊M4(2)⋊39C2 = C42.308C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):39C2128,1725
C4⋊M4(2)⋊40C2 = C42.310C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2):40C2128,1727
C4⋊M4(2)⋊41C2 = C42.677C23φ: trivial image32C4:M4(2):41C2128,1652
C4⋊M4(2)⋊42C2 = C42.681C23φ: trivial image64C4:M4(2):42C2128,1663

Non-split extensions G=N.Q with N=C4⋊M4(2) and Q=C2
extensionφ:Q→Out NdρLabelID
C4⋊M4(2).1C2 = C42.32Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)164C4:M4(2).1C2128,834
C4⋊M4(2).2C2 = C42.220D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).2C2128,1810
C4⋊M4(2).3C2 = C42.303D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).3C2128,1987
C4⋊M4(2).4C2 = C42.5Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2).4C2128,18
C4⋊M4(2).5C2 = C42.27D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).5C2128,24
C4⋊M4(2).6C2 = C42.388D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).6C2128,31
C4⋊M4(2).7C2 = C42.389D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).7C2128,33
C4⋊M4(2).8C2 = C42.10Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2).8C2128,35
C4⋊M4(2).9C2 = C42.30D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).9C2128,39
C4⋊M4(2).10C2 = C42.32D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).10C2128,41
C4⋊M4(2).11C2 = C42.C8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)164C4:M4(2).11C2128,59
C4⋊M4(2).12C2 = Q8⋊M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).12C2128,219
C4⋊M4(2).13C2 = C42.316D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).13C2128,225
C4⋊M4(2).14C2 = C42.414D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).14C2128,278
C4⋊M4(2).15C2 = C42.415D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).15C2128,280
C4⋊M4(2).16C2 = C42.416D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).16C2128,281
C4⋊M4(2).17C2 = C42.79D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).17C2128,282
C4⋊M4(2).18C2 = C42.86D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).18C2128,291
C4⋊M4(2).19C2 = C42.88D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).19C2128,293
C4⋊M4(2).20C2 = C8⋊8M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).20C2128,298
C4⋊M4(2).21C2 = C8⋊7M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).21C2128,299
C4⋊M4(2).22C2 = C8⋊1M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).22C2128,301
C4⋊M4(2).23C2 = C42.90D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).23C2128,302
C4⋊M4(2).24C2 = C42.91D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).24C2128,303
C4⋊M4(2).25C2 = C42.21Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).25C2128,306
C4⋊M4(2).26C2 = C42.97D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).26C2128,533
C4⋊M4(2).27C2 = C42.322D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).27C2128,569
C4⋊M4(2).28C2 = C42.104D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).28C2128,570
C4⋊M4(2).29C2 = C42.324D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).29C2128,580
C4⋊M4(2).30C2 = C42.106D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).30C2128,581
C4⋊M4(2).31C2 = C42.430D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).31C2128,682
C4⋊M4(2).32C2 = C42.114D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).32C2128,698
C4⋊M4(2).33C2 = C42⋊16Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2).33C2128,726
C4⋊M4(2).34C2 = C42⋊Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)32C4:M4(2).34C2128,727
C4⋊M4(2).35C2 = M4(2)⋊8Q8φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).35C2128,729
C4⋊M4(2).36C2 = C42.128D4φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).36C2128,730
C4⋊M4(2).37C2 = C42.287C23φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).37C2128,1693
C4⋊M4(2).38C2 = Q8×M4(2)φ: C2/C1 → C2 ⊆ Out C4⋊M4(2)64C4:M4(2).38C2128,1695
C4⋊M4(2).39C2 = C42.286C23φ: trivial image64C4:M4(2).39C2128,1692

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