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Extensions 1→N→G→Q→1 with N=C12⋊D4 and Q=C2

Direct product G=N×Q with N=C12⋊D4 and Q=C2
dρLabelID
C2×C12⋊D496C2xC12:D4192,1065

Semidirect products G=N:Q with N=C12⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
C12⋊D4⋊1C2 = D4⋊D12φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:1C2192,332
C12⋊D4⋊2C2 = D6⋊D8φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:2C2192,334
C12⋊D4⋊3C2 = D4⋊3D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:3C2192,340
C12⋊D4⋊4C2 = C3⋊C8⋊D4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:4C2192,341
C12⋊D4⋊5C2 = Q8⋊4D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:5C2192,369
C12⋊D4⋊6C2 = C24⋊7D4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:6C2192,424
C12⋊D4⋊7C2 = D6⋊2D8φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:7C2192,442
C12⋊D4⋊8C2 = C6.2- 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:8C2192,1066
C12⋊D4⋊9C2 = C6.2+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:9C2192,1069
C12⋊D4⋊10C2 = C6.112+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:10C2192,1073
C12⋊D4⋊11C2 = C42⋊11D6φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:11C2192,1084
C12⋊D4⋊12C2 = C42.95D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:12C2192,1089
C12⋊D4⋊13C2 = C42.97D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:13C2192,1091
C12⋊D4⋊14C2 = D4×D12φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:14C2192,1108
C12⋊D4⋊15C2 = D4⋊5D12φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:15C2192,1113
C12⋊D4⋊16C2 = C42.116D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:16C2192,1121
C12⋊D4⋊17C2 = Q8⋊6D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:17C2192,1135
C12⋊D4⋊18C2 = Q8⋊7D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:18C2192,1136
C12⋊D4⋊19C2 = Dic6⋊20D4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:19C2192,1158
C12⋊D4⋊20C2 = S3×C4⋊D4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:20C2192,1163
C12⋊D4⋊21C2 = C6.382+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:21C2192,1166
C12⋊D4⋊22C2 = D12⋊19D4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:22C2192,1168
C12⋊D4⋊23C2 = C4⋊C4⋊26D6φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:23C2192,1186
C12⋊D4⋊24C2 = C6.172- 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:24C2192,1188
C12⋊D4⋊25C2 = D12⋊21D4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:25C2192,1189
C12⋊D4⋊26C2 = Dic6⋊22D4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:26C2192,1192
C12⋊D4⋊27C2 = C6.562+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:27C2192,1203
C12⋊D4⋊28C2 = C6.592+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:28C2192,1206
C12⋊D4⋊29C2 = C6.1202+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:29C2192,1212
C12⋊D4⋊30C2 = C6.1212+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:30C2192,1213
C12⋊D4⋊31C2 = C6.662+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:31C2192,1222
C12⋊D4⋊32C2 = C6.682+ 1+4φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:32C2192,1225
C12⋊D4⋊33C2 = C42.153D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:33C2192,1254
C12⋊D4⋊34C2 = C42.155D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:34C2192,1256
C12⋊D4⋊35C2 = C42.158D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:35C2192,1259
C12⋊D4⋊36C2 = C42⋊25D6φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:36C2192,1263
C12⋊D4⋊37C2 = C42.163D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:37C2192,1268
C12⋊D4⋊38C2 = C42⋊27D6φ: C2/C1 → C2 ⊆ Out C12⋊D448C12:D4:38C2192,1270
C12⋊D4⋊39C2 = C42.240D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:39C2192,1284
C12⋊D4⋊40C2 = D12⋊12D4φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:40C2192,1285
C12⋊D4⋊41C2 = C42.179D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4:41C2192,1293
C12⋊D4⋊42C2 = C42⋊10D6φ: trivial image48C12:D4:42C2192,1083
C12⋊D4⋊43C2 = C42.228D6φ: trivial image96C12:D4:43C2192,1107

Non-split extensions G=N.Q with N=C12⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
C12⋊D4.1C2 = Q8⋊3D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.1C2192,365
C12⋊D4.2C2 = D6⋊2SD16φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.2C2192,366
C12⋊D4.3C2 = C3⋊(C8⋊D4)φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.3C2192,371
C12⋊D4.4C2 = D6.4SD16φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.4C2192,422
C12⋊D4.5C2 = C8⋊8D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.5C2192,423
C12⋊D4.6C2 = C4.Q8⋊S3φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.6C2192,425
C12⋊D4.7C2 = D6.5D8φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.7C2192,441
C12⋊D4.8C2 = C2.D8⋊S3φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.8C2192,444
C12⋊D4.9C2 = C8⋊3D12φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.9C2192,445
C12⋊D4.10C2 = C42.133D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.10C2192,1141
C12⋊D4.11C2 = C42.237D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.11C2192,1250
C12⋊D4.12C2 = C42.150D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.12C2192,1251
C12⋊D4.13C2 = C42.178D6φ: C2/C1 → C2 ⊆ Out C12⋊D496C12:D4.13C2192,1292
C12⋊D4.14C2 = C42.131D6φ: trivial image96C12:D4.14C2192,1139

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