# Extensions 1→N→G→Q→1 with N=C42⋊C2 and Q=C4

Direct product G=N×Q with N=C42⋊C2 and Q=C4
dρLabelID
C4×C42⋊C264C4xC4^2:C2128,1002

Semidirect products G=N:Q with N=C42⋊C2 and Q=C4
extensionφ:Q→Out NdρLabelID
C42⋊C21C4 = C24.53D4φ: C4/C1C4 ⊆ Out C42⋊C232C4^2:C2:1C4128,233
C42⋊C22C4 = C24.150D4φ: C4/C1C4 ⊆ Out C42⋊C216C4^2:C2:2C4128,236
C42⋊C23C4 = C24.58D4φ: C4/C1C4 ⊆ Out C42⋊C232C4^2:C2:3C4128,245
C42⋊C24C4 = C24.59D4φ: C4/C1C4 ⊆ Out C42⋊C232C4^2:C2:4C4128,248
C42⋊C25C4 = C24.C23φ: C4/C1C4 ⊆ Out C42⋊C2168+C4^2:C2:5C4128,560
C42⋊C26C4 = C4○C2≀C4φ: C4/C1C4 ⊆ Out C42⋊C2164C4^2:C2:6C4128,852
C42⋊C27C4 = C2≀C4⋊C2φ: C4/C1C4 ⊆ Out C42⋊C2168+C4^2:C2:7C4128,854
C42⋊C28C4 = C23.(C2×D4)φ: C4/C1C4 ⊆ Out C42⋊C2328-C4^2:C2:8C4128,855
C42⋊C29C4 = C24.39D4φ: C4/C1C4 ⊆ Out C42⋊C2168+C4^2:C2:9C4128,859
C42⋊C210C4 = C4.4D4⋊C4φ: C4/C1C4 ⊆ Out C42⋊C2168+C4^2:C2:10C4128,860
C42⋊C211C4 = C4⋊Q8⋊C4φ: C4/C1C4 ⊆ Out C42⋊C2328-C4^2:C2:11C4128,861
C42⋊C212C4 = C2×C4.9C42φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2:12C4128,462
C42⋊C213C4 = C2×C426C4φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2:13C4128,464
C42⋊C214C4 = C24.63D4φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2:14C4128,465
C42⋊C215C4 = C24.132D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:15C4128,467
C42⋊C216C4 = C24.152D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:16C4128,468
C42⋊C217C4 = C24.162C23φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2:17C4128,472
C42⋊C218C4 = C24.69D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:18C4128,557
C42⋊C219C4 = C24.70D4φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2:19C4128,558
C42⋊C220C4 = (C2×C42)⋊C4φ: C4/C2C2 ⊆ Out C42⋊C2164C4^2:C2:20C4128,559
C42⋊C221C4 = C24.524C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:21C4128,1006
C42⋊C222C4 = C23.178C24φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:22C4128,1028
C42⋊C223C4 = C432C2φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:23C4128,1030
C42⋊C224C4 = C24.192C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:24C4128,1046
C42⋊C225C4 = C23.199C24φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:25C4128,1049
C42⋊C226C4 = C23.225C24φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:26C4128,1075
C42⋊C227C4 = C24.208C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:27C4128,1078
C42⋊C228C4 = C23.229C24φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2:28C4128,1079

Non-split extensions G=N.Q with N=C42⋊C2 and Q=C4
extensionφ:Q→Out NdρLabelID
C42⋊C2.1C4 = C23.7M4(2)φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.1C4128,55
C42⋊C2.2C4 = C22⋊C4.C8φ: C4/C1C4 ⊆ Out C42⋊C2324C4^2:C2.2C4128,60
C42⋊C2.3C4 = C42.406D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.3C4128,258
C42⋊C2.4C4 = C42.68D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.4C4128,263
C42⋊C2.5C4 = C42.74D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.5C4128,269
C42⋊C2.6C4 = C42.412D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.6C4128,276
C42⋊C2.7C4 = C42.81D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.7C4128,284
C42⋊C2.8C4 = C42.88D4φ: C4/C1C4 ⊆ Out C42⋊C264C4^2:C2.8C4128,293
C42⋊C2.9C4 = (C2×Q8).211D4φ: C4/C1C4 ⊆ Out C42⋊C2328-C4^2:C2.9C4128,562
C42⋊C2.10C4 = C4⋊Q8.C4φ: C4/C1C4 ⊆ Out C42⋊C2328-C4^2:C2.10C4128,865
C42⋊C2.11C4 = C41D4.C4φ: C4/C1C4 ⊆ Out C42⋊C2168+C4^2:C2.11C4128,866
C42⋊C2.12C4 = (C2×D4).137D4φ: C4/C1C4 ⊆ Out C42⋊C2328-C4^2:C2.12C4128,867
C42⋊C2.13C4 = M4(2).C8φ: C4/C2C2 ⊆ Out C42⋊C2324C4^2:C2.13C4128,110
C42⋊C2.14C4 = M5(2)⋊7C4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.14C4128,111
C42⋊C2.15C4 = C42.455D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.15C4128,208
C42⋊C2.16C4 = C42.397D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.16C4128,209
C42⋊C2.17C4 = C42.374D4φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.17C4128,220
C42⋊C2.18C4 = D44M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.18C4128,221
C42⋊C2.19C4 = C2×M4(2)⋊4C4φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2.19C4128,475
C42⋊C2.20C4 = C8.23C42φ: C4/C2C2 ⊆ Out C42⋊C2324C4^2:C2.20C4128,842
C42⋊C2.21C4 = C4⋊C4.7C8φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.21C4128,883
C42⋊C2.22C4 = M4(2).1C8φ: C4/C2C2 ⊆ Out C42⋊C2324C4^2:C2.22C4128,885
C42⋊C2.23C4 = C8.12M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.23C4128,896
C42⋊C2.24C4 = C8.19M4(2)φ: C4/C2C2 ⊆ Out C42⋊C2324C4^2:C2.24C4128,898
C42⋊C2.25C4 = M4(2)○2M4(2)φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2.25C4128,1605
C42⋊C2.26C4 = C2×C42.6C22φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.26C4128,1636
C42⋊C2.27C4 = C42.257C23φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2.27C4128,1637
C42⋊C2.28C4 = C2×C42.7C22φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.28C4128,1651
C42⋊C2.29C4 = C42.259C23φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2.29C4128,1653
C42⋊C2.30C4 = C42.262C23φ: C4/C2C2 ⊆ Out C42⋊C232C4^2:C2.30C4128,1656
C42⋊C2.31C4 = C42.290C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.31C4128,1697
C42⋊C2.32C4 = D46M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.32C4128,1702
C42⋊C2.33C4 = Q86M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.33C4128,1703
C42⋊C2.34C4 = C42.697C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.34C4128,1720
C42⋊C2.35C4 = C42.698C23φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.35C4128,1721
C42⋊C2.36C4 = D48M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.36C4128,1722
C42⋊C2.37C4 = Q87M4(2)φ: C4/C2C2 ⊆ Out C42⋊C264C4^2:C2.37C4128,1723
C42⋊C2.38C4 = C162M5(2)φ: trivial image64C4^2:C2.38C4128,840
C42⋊C2.39C4 = C2×C82M4(2)φ: trivial image64C4^2:C2.39C4128,1604
C42⋊C2.40C4 = C8×C4○D4φ: trivial image64C4^2:C2.40C4128,1696

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