# Extensions 1→N→G→Q→1 with N=C42.12C4 and Q=C2

Direct product G=N×Q with N=C42.12C4 and Q=C2
dρLabelID
C2×C42.12C464C2xC4^2.12C4128,1649

Semidirect products G=N:Q with N=C42.12C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C42.12C41C2 = C42.371D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:1C2128,190
C42.12C42C2 = C42.393D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:2C2128,192
C42.12C43C2 = C42.395D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:3C2128,201
C42.12C44C2 = C42.372D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:4C2128,205
C42.12C45C2 = C42.455D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:5C2128,208
C42.12C46C2 = C42.397D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:6C2128,209
C42.12C47C2 = C42.398D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:7C2128,210
C42.12C48C2 = C42.45D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:8C2128,212
C42.12C49C2 = C42.373D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:9C2128,214
C42.12C410C2 = C42.400D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:10C2128,216
C42.12C411C2 = D4⋊M4(2)φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:11C2128,218
C42.12C412C2 = C42.374D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:12C2128,220
C42.12C413C2 = C42.52D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:13C2128,227
C42.12C414C2 = C42.53D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:14C2128,228
C42.12C415C2 = C42.375D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:15C2128,232
C42.12C416C2 = C42.403D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:16C2128,234
C42.12C417C2 = C42.61D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:17C2128,249
C42.12C418C2 = C42.63D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:18C2128,253
C42.12C419C2 = C42.409D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:19C2128,272
C42.12C420C2 = C42.411D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:20C2128,275
C42.12C421C2 = C42.413D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:21C2128,277
C42.12C422C2 = C42.417D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:22C2128,285
C42.12C423C2 = C42.691C23φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:23C2128,1704
C42.12C424C2 = C42.697C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:24C2128,1720
C42.12C425C2 = C42.221D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:25C2128,1832
C42.12C426C2 = C42.263D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:26C2128,1937
C42.12C427C2 = C42.278D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:27C2128,1958
C42.12C428C2 = C42.384D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:28C2128,1834
C42.12C429C2 = C42.225D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:29C2128,1837
C42.12C430C2 = C42.450D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:30C2128,1838
C42.12C431C2 = C42.451D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:31C2128,1839
C42.12C432C2 = C42.226D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:32C2128,1840
C42.12C433C2 = C42.265D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:33C2128,1939
C42.12C434C2 = C42.268D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:34C2128,1942
C42.12C435C2 = C42.269D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:35C2128,1943
C42.12C436C2 = C42.270D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:36C2128,1944
C42.12C437C2 = C42.280D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:37C2128,1960
C42.12C438C2 = C42.284D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:38C2128,1964
C42.12C439C2 = C42.285D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:39C2128,1965
C42.12C440C2 = C42.222D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:40C2128,1833
C42.12C441C2 = C42.223D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:41C2128,1835
C42.12C442C2 = C42.264D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:42C2128,1938
C42.12C443C2 = C42.266D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:43C2128,1940
C42.12C444C2 = C42.279D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:44C2128,1959
C42.12C445C2 = C42.677C23φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:45C2128,1652
C42.12C446C2 = C42.260C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:46C2128,1654
C42.12C447C2 = C42.262C23φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:47C2128,1656
C42.12C448C2 = C42.678C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:48C2128,1657
C42.12C449C2 = C42.290C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:49C2128,1697
C42.12C450C2 = C42.293C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:50C2128,1700
C42.12C451C2 = C42.294C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:51C2128,1701
C42.12C452C2 = D47M4(2)φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:52C2128,1706
C42.12C453C2 = C42.693C23φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4:53C2128,1707
C42.12C454C2 = C42.694C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:54C2128,1711
C42.12C455C2 = C42.301C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:55C2128,1713
C42.12C456C2 = C42.698C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:56C2128,1721
C42.12C457C2 = D48M4(2)φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:57C2128,1722
C42.12C458C2 = Q87M4(2)φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:58C2128,1723
C42.12C459C2 = C42.308C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:59C2128,1725
C42.12C460C2 = C42.309C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4:60C2128,1726
C42.12C461C2 = C8×C4○D4φ: trivial image64C4^2.12C4:61C2128,1696

Non-split extensions G=N.Q with N=C42.12C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C42.12C4.1C2 = C421C8φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.1C2128,6
C42.12C4.2C2 = C42.20D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.2C2128,7
C42.12C4.3C2 = C426C8φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.3C2128,8
C42.12C4.4C2 = M4(2)⋊C8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.4C2128,10
C42.12C4.5C2 = C42.2Q8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.5C2128,13
C42.12C4.6C2 = C42.3Q8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.6C2128,15
C42.12C4.7C2 = C42.5Q8φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.7C2128,18
C42.12C4.8C2 = C42.23D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.8C2128,19
C42.12C4.9C2 = C42.388D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.9C2128,31
C42.12C4.10C2 = C42.389D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.10C2128,33
C42.12C4.11C2 = C42.370D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.11C2128,34
C42.12C4.12C2 = C42.10Q8φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.12C2128,35
C42.12C4.13C2 = C42.394D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.13C2128,193
C42.12C4.14C2 = C42.396D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.14C2128,202
C42.12C4.15C2 = C42.399D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.15C2128,211
C42.12C4.16C2 = C42.46D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.16C2128,213
C42.12C4.17C2 = C42.401D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.17C2128,217
C42.12C4.18C2 = Q8⋊M4(2)φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.18C2128,219
C42.12C4.19C2 = C42.54D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.19C2128,229
C42.12C4.20C2 = C42.404D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.20C2128,235
C42.12C4.21C2 = C42.62D4φ: C2/C1C2 ⊆ Out C42.12C432C4^2.12C4.21C2128,250
C42.12C4.22C2 = C42.410D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.22C2128,274
C42.12C4.23C2 = C42.412D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.23C2128,276
C42.12C4.24C2 = C42.414D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.24C2128,278
C42.12C4.25C2 = C42.415D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.25C2128,280
C42.12C4.26C2 = C42.416D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.26C2128,281
C42.12C4.27C2 = C42.418D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.27C2128,286
C42.12C4.28C2 = C42.42Q8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.28C2128,296
C42.12C4.29C2 = M4(2)⋊1C8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.29C2128,297
C42.12C4.30C2 = C42.Q8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.30C2128,304
C42.12C4.31C2 = C42.21Q8φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.31C2128,306
C42.12C4.32C2 = C42.695C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.32C2128,1714
C42.12C4.33C2 = C42.91D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.33C2128,303
C42.12C4.34C2 = C42.224D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.34C2128,1836
C42.12C4.35C2 = C42.267D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.35C2128,1941
C42.12C4.36C2 = C42.282D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.36C2128,1962
C42.12C4.37C2 = C42.92D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.37C2128,305
C42.12C4.38C2 = C42.283D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.38C2128,1963
C42.12C4.39C2 = C42.90D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.39C2128,302
C42.12C4.40C2 = C42.281D4φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.40C2128,1961
C42.12C4.41C2 = C89M4(2)φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.41C2128,183
C42.12C4.42C2 = C23.27C42φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.42C2128,184
C42.12C4.43C2 = C8215C2φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.43C2128,185
C42.12C4.44C2 = C822C2φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.44C2128,186
C42.12C4.45C2 = C42.302C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.45C2128,1715
C42.12C4.46C2 = Q8.4M4(2)φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.46C2128,1716
C42.12C4.47C2 = C42.696C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.47C2128,1717
C42.12C4.48C2 = C42.304C23φ: C2/C1C2 ⊆ Out C42.12C464C4^2.12C4.48C2128,1718
C42.12C4.49C2 = C8×M4(2)φ: trivial image64C4^2.12C4.49C2128,181
C42.12C4.50C2 = C82⋊C2φ: trivial image64C4^2.12C4.50C2128,182

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