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Extensions 1→N→G→Q→1 with N=C6 and Q=2- 1+4

Direct product G=N×Q with N=C6 and Q=2- 1+4
dρLabelID
C6×2- 1+496C6xES-(2,2)192,1535

Semidirect products G=N:Q with N=C6 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C6⋊12- 1+4 = C2×Q8.15D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6:1ES-(2,2)192,1519
C6⋊22- 1+4 = C2×Q8○D12φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6:2ES-(2,2)192,1522

Non-split extensions G=N.Q with N=C6 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C6.12- 1+4 = C6.72+ 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.1ES-(2,2)192,1059
C6.22- 1+4 = C6.82+ 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.2ES-(2,2)192,1063
C6.32- 1+4 = C6.2- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.3ES-(2,2)192,1066
C6.42- 1+4 = C6.2+ 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.4ES-(2,2)192,1069
C6.52- 1+4 = C6.52- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.5ES-(2,2)192,1072
C6.62- 1+4 = C6.62- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.6ES-(2,2)192,1074
C6.72- 1+4 = C42.122D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.7ES-(2,2)192,1127
C6.82- 1+4 = Q8⋊6Dic6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C6192C6.8ES-(2,2)192,1128
C6.92- 1+4 = C42.125D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.9ES-(2,2)192,1131
C6.102- 1+4 = C42.126D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.10ES-(2,2)192,1133
C6.112- 1+4 = Q8⋊6D12φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.11ES-(2,2)192,1135
C6.122- 1+4 = C42.132D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.12ES-(2,2)192,1140
C6.132- 1+4 = C42.133D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.13ES-(2,2)192,1141
C6.142- 1+4 = C42.134D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.14ES-(2,2)192,1142
C6.152- 1+4 = C6.152- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.15ES-(2,2)192,1184
C6.162- 1+4 = C6.162- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.16ES-(2,2)192,1187
C6.172- 1+4 = C6.172- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.17ES-(2,2)192,1188
C6.182- 1+4 = D12⋊22D4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.18ES-(2,2)192,1190
C6.192- 1+4 = Dic6⋊22D4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.19ES-(2,2)192,1192
C6.202- 1+4 = C6.202- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.20ES-(2,2)192,1197
C6.212- 1+4 = C6.212- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.21ES-(2,2)192,1198
C6.222- 1+4 = C6.222- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.22ES-(2,2)192,1199
C6.232- 1+4 = C6.232- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.23ES-(2,2)192,1200
C6.242- 1+4 = C6.242- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.24ES-(2,2)192,1202
C6.252- 1+4 = C6.252- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.25ES-(2,2)192,1205
C6.262- 1+4 = C6.592+ 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.26ES-(2,2)192,1206
C6.272- 1+4 = C42.147D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C6192C6.27ES-(2,2)192,1245
C6.282- 1+4 = C42.150D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.28ES-(2,2)192,1251
C6.292- 1+4 = C42.151D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.29ES-(2,2)192,1252
C6.302- 1+4 = C42.154D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.30ES-(2,2)192,1255
C6.312- 1+4 = C42.157D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.31ES-(2,2)192,1258
C6.322- 1+4 = C42.158D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.32ES-(2,2)192,1259
C6.332- 1+4 = Dic6⋊8Q8φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C6192C6.33ES-(2,2)192,1280
C6.342- 1+4 = C42.171D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.34ES-(2,2)192,1283
C6.352- 1+4 = D12⋊12D4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.35ES-(2,2)192,1285
C6.362- 1+4 = D12⋊8Q8φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.36ES-(2,2)192,1286
C6.372- 1+4 = C42.174D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.37ES-(2,2)192,1288
C6.382- 1+4 = C42.176D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.38ES-(2,2)192,1290
C6.392- 1+4 = C42.177D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.39ES-(2,2)192,1291
C6.402- 1+4 = C42.178D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.40ES-(2,2)192,1292
C6.412- 1+4 = C42.180D6φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.41ES-(2,2)192,1294
C6.422- 1+4 = C6.422- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.42ES-(2,2)192,1371
C6.432- 1+4 = Q8×C3⋊D4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.43ES-(2,2)192,1374
C6.442- 1+4 = C6.442- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.44ES-(2,2)192,1375
C6.452- 1+4 = C6.452- 1+4φ: 2- 1+4/C2×Q8 → C2 ⊆ Aut C696C6.45ES-(2,2)192,1376
C6.462- 1+4 = C42.87D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.46ES-(2,2)192,1075
C6.472- 1+4 = C42.89D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.47ES-(2,2)192,1077
C6.482- 1+4 = C42.90D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.48ES-(2,2)192,1078
C6.492- 1+4 = C42.91D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.49ES-(2,2)192,1082
C6.502- 1+4 = C42.92D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.50ES-(2,2)192,1085
C6.512- 1+4 = C42.94D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.51ES-(2,2)192,1088
C6.522- 1+4 = C42.96D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.52ES-(2,2)192,1090
C6.532- 1+4 = C42.98D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.53ES-(2,2)192,1092
C6.542- 1+4 = C42.99D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.54ES-(2,2)192,1093
C6.552- 1+4 = D4×Dic6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.55ES-(2,2)192,1096
C6.562- 1+4 = C42.105D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.56ES-(2,2)192,1100
C6.572- 1+4 = C42.106D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.57ES-(2,2)192,1101
C6.582- 1+4 = C42.108D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.58ES-(2,2)192,1105
C6.592- 1+4 = D12⋊24D4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.59ES-(2,2)192,1110
C6.602- 1+4 = Dic6⋊23D4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.60ES-(2,2)192,1111
C6.612- 1+4 = D4⋊6D12φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.61ES-(2,2)192,1114
C6.622- 1+4 = C42.115D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.62ES-(2,2)192,1120
C6.632- 1+4 = C42.118D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.63ES-(2,2)192,1123
C6.642- 1+4 = Dic6⋊10Q8φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C6192C6.64ES-(2,2)192,1126
C6.652- 1+4 = Q8⋊7Dic6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C6192C6.65ES-(2,2)192,1129
C6.662- 1+4 = Q8×D12φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.66ES-(2,2)192,1134
C6.672- 1+4 = C42.135D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.67ES-(2,2)192,1143
C6.682- 1+4 = C6.322+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.68ES-(2,2)192,1156
C6.692- 1+4 = Dic6⋊19D4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.69ES-(2,2)192,1157
C6.702- 1+4 = C6.702- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.70ES-(2,2)192,1161
C6.712- 1+4 = C6.712- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.71ES-(2,2)192,1162
C6.722- 1+4 = C6.722- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.72ES-(2,2)192,1167
C6.732- 1+4 = C6.732- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.73ES-(2,2)192,1170
C6.742- 1+4 = C6.492+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.74ES-(2,2)192,1180
C6.752- 1+4 = C6.752- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.75ES-(2,2)192,1182
C6.762- 1+4 = Dic6⋊21D4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.76ES-(2,2)192,1191
C6.772- 1+4 = C6.772- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.77ES-(2,2)192,1201
C6.782- 1+4 = C6.782- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.78ES-(2,2)192,1204
C6.792- 1+4 = C6.792- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.79ES-(2,2)192,1207
C6.802- 1+4 = C6.802- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.80ES-(2,2)192,1209
C6.812- 1+4 = C6.812- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.81ES-(2,2)192,1210
C6.822- 1+4 = C6.822- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.82ES-(2,2)192,1214
C6.832- 1+4 = C6.632+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.83ES-(2,2)192,1219
C6.842- 1+4 = C6.652+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.84ES-(2,2)192,1221
C6.852- 1+4 = C6.852- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.85ES-(2,2)192,1224
C6.862- 1+4 = C6.692+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.86ES-(2,2)192,1226
C6.872- 1+4 = C42.137D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.87ES-(2,2)192,1228
C6.882- 1+4 = C42.139D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.88ES-(2,2)192,1230
C6.892- 1+4 = C42.140D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.89ES-(2,2)192,1231
C6.902- 1+4 = C42.141D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.90ES-(2,2)192,1234
C6.912- 1+4 = Dic6⋊10D4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.91ES-(2,2)192,1236
C6.922- 1+4 = C42.144D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.92ES-(2,2)192,1241
C6.932- 1+4 = C42.145D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.93ES-(2,2)192,1243
C6.942- 1+4 = Dic6⋊7Q8φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C6192C6.94ES-(2,2)192,1244
C6.952- 1+4 = C42.148D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.95ES-(2,2)192,1248
C6.962- 1+4 = C42.152D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.96ES-(2,2)192,1253
C6.972- 1+4 = C42.156D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.97ES-(2,2)192,1257
C6.982- 1+4 = C42.159D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.98ES-(2,2)192,1260
C6.992- 1+4 = C42.160D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.99ES-(2,2)192,1261
C6.1002- 1+4 = C42.161D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.100ES-(2,2)192,1266
C6.1012- 1+4 = C42.162D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.101ES-(2,2)192,1267
C6.1022- 1+4 = C42.164D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.102ES-(2,2)192,1269
C6.1032- 1+4 = C42.165D6φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.103ES-(2,2)192,1271
C6.1042- 1+4 = C6.1042- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.104ES-(2,2)192,1383
C6.1052- 1+4 = C6.1052- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.105ES-(2,2)192,1384
C6.1062- 1+4 = C6.1442+ 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.106ES-(2,2)192,1386
C6.1072- 1+4 = C6.1072- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.107ES-(2,2)192,1390
C6.1082- 1+4 = C6.1082- 1+4φ: 2- 1+4/C4○D4 → C2 ⊆ Aut C696C6.108ES-(2,2)192,1392
C6.1092- 1+4 = C3×C23.32C23central extension (φ=1)96C6.109ES-(2,2)192,1408
C6.1102- 1+4 = C3×C23.33C23central extension (φ=1)96C6.110ES-(2,2)192,1409
C6.1112- 1+4 = C3×C23.38C23central extension (φ=1)96C6.111ES-(2,2)192,1425
C6.1122- 1+4 = C3×C22.31C24central extension (φ=1)96C6.112ES-(2,2)192,1426
C6.1132- 1+4 = C3×C22.33C24central extension (φ=1)96C6.113ES-(2,2)192,1428
C6.1142- 1+4 = C3×C22.35C24central extension (φ=1)96C6.114ES-(2,2)192,1430
C6.1152- 1+4 = C3×C22.36C24central extension (φ=1)96C6.115ES-(2,2)192,1431
C6.1162- 1+4 = C3×C23.41C23central extension (φ=1)96C6.116ES-(2,2)192,1433
C6.1172- 1+4 = C3×D4⋊6D4central extension (φ=1)96C6.117ES-(2,2)192,1436
C6.1182- 1+4 = C3×Q8⋊5D4central extension (φ=1)96C6.118ES-(2,2)192,1437
C6.1192- 1+4 = C3×D4×Q8central extension (φ=1)96C6.119ES-(2,2)192,1438
C6.1202- 1+4 = C3×C22.46C24central extension (φ=1)96C6.120ES-(2,2)192,1441
C6.1212- 1+4 = C3×C22.50C24central extension (φ=1)96C6.121ES-(2,2)192,1445
C6.1222- 1+4 = C3×Q8⋊3Q8central extension (φ=1)192C6.122ES-(2,2)192,1446
C6.1232- 1+4 = C3×C22.56C24central extension (φ=1)96C6.123ES-(2,2)192,1451
C6.1242- 1+4 = C3×C22.57C24central extension (φ=1)96C6.124ES-(2,2)192,1452
C6.1252- 1+4 = C3×C22.58C24central extension (φ=1)192C6.125ES-(2,2)192,1453

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