# Extensions 1→N→G→Q→1 with N=C24 and Q=C23

Direct product G=N×Q with N=C24 and Q=C23
dρLabelID
C23×C24192C2^3xC24192,1454

Semidirect products G=N:Q with N=C24 and Q=C23
extensionφ:Q→Aut NdρLabelID
C24⋊C23 = S3×C8⋊C22φ: C23/C1C23 ⊆ Aut C24248+C24:C2^3192,1331
C242C23 = C2×C8⋊D6φ: C23/C2C22 ⊆ Aut C2448C24:2C2^3192,1305
C243C23 = C2×S3×D8φ: C23/C2C22 ⊆ Aut C2448C24:3C2^3192,1313
C244C23 = C2×Q83D6φ: C23/C2C22 ⊆ Aut C2448C24:4C2^3192,1318
C245C23 = C2×D8⋊S3φ: C23/C2C22 ⊆ Aut C2448C24:5C2^3192,1314
C246C23 = C2×S3×SD16φ: C23/C2C22 ⊆ Aut C2448C24:6C2^3192,1317
C247C23 = C6×C8⋊C22φ: C23/C2C22 ⊆ Aut C2448C24:7C2^3192,1462
C248C23 = C2×S3×M4(2)φ: C23/C2C22 ⊆ Aut C2448C24:8C2^3192,1302
C249C23 = C22×D24φ: C23/C22C2 ⊆ Aut C2496C24:9C2^3192,1299
C2410C23 = C22×C24⋊C2φ: C23/C22C2 ⊆ Aut C2496C24:10C2^3192,1298
C2411C23 = C2×C6×D8φ: C23/C22C2 ⊆ Aut C2496C24:11C2^3192,1458
C2412C23 = S3×C22×C8φ: C23/C22C2 ⊆ Aut C2496C24:12C2^3192,1295
C2413C23 = C22×C8⋊S3φ: C23/C22C2 ⊆ Aut C2496C24:13C2^3192,1296
C2414C23 = C2×C6×SD16φ: C23/C22C2 ⊆ Aut C2496C24:14C2^3192,1459
C2415C23 = C2×C6×M4(2)φ: C23/C22C2 ⊆ Aut C2496C24:15C2^3192,1455

Non-split extensions G=N.Q with N=C24 and Q=C23
extensionφ:Q→Aut NdρLabelID
C24.1C23 = D84D6φ: C23/C1C23 ⊆ Aut C24488-C24.1C2^3192,1332
C24.2C23 = D85D6φ: C23/C1C23 ⊆ Aut C24488+C24.2C2^3192,1333
C24.3C23 = D86D6φ: C23/C1C23 ⊆ Aut C24488-C24.3C2^3192,1334
C24.4C23 = S3×C8.C22φ: C23/C1C23 ⊆ Aut C24488-C24.4C2^3192,1335
C24.5C23 = D24⋊C22φ: C23/C1C23 ⊆ Aut C24488+C24.5C2^3192,1336
C24.6C23 = C24.C23φ: C23/C1C23 ⊆ Aut C24488+C24.6C2^3192,1337
C24.7C23 = SD16.D6φ: C23/C1C23 ⊆ Aut C24968-C24.7C2^3192,1338
C24.8C23 = C2×C8.D6φ: C23/C2C22 ⊆ Aut C2496C24.8C2^3192,1306
C24.9C23 = C24.9C23φ: C23/C2C22 ⊆ Aut C24484C24.9C2^3192,1307
C24.10C23 = D4.11D12φ: C23/C2C22 ⊆ Aut C24484C24.10C2^3192,1310
C24.11C23 = D4.12D12φ: C23/C2C22 ⊆ Aut C24484+C24.11C2^3192,1311
C24.12C23 = D4.13D12φ: C23/C2C22 ⊆ Aut C24964-C24.12C2^3192,1312
C24.13C23 = S3×D16φ: C23/C2C22 ⊆ Aut C24484+C24.13C2^3192,469
C24.14C23 = D8⋊D6φ: C23/C2C22 ⊆ Aut C24484C24.14C2^3192,470
C24.15C23 = D163S3φ: C23/C2C22 ⊆ Aut C24964-C24.15C2^3192,471
C24.16C23 = S3×SD32φ: C23/C2C22 ⊆ Aut C24484C24.16C2^3192,472
C24.17C23 = D48⋊C2φ: C23/C2C22 ⊆ Aut C24484+C24.17C2^3192,473
C24.18C23 = SD32⋊S3φ: C23/C2C22 ⊆ Aut C24964-C24.18C2^3192,474
C24.19C23 = D6.2D8φ: C23/C2C22 ⊆ Aut C24964C24.19C2^3192,475
C24.20C23 = S3×Q32φ: C23/C2C22 ⊆ Aut C24964-C24.20C2^3192,476
C24.21C23 = Q32⋊S3φ: C23/C2C22 ⊆ Aut C24964C24.21C2^3192,477
C24.22C23 = D485C2φ: C23/C2C22 ⊆ Aut C24964+C24.22C2^3192,478
C24.23C23 = C2×C3⋊D16φ: C23/C2C22 ⊆ Aut C2496C24.23C2^3192,705
C24.24C23 = D8.D6φ: C23/C2C22 ⊆ Aut C24484C24.24C2^3192,706
C24.25C23 = C2×D8.S3φ: C23/C2C22 ⊆ Aut C2496C24.25C2^3192,707
C24.26C23 = C2×C8.6D6φ: C23/C2C22 ⊆ Aut C2496C24.26C2^3192,737
C24.27C23 = C24.27C23φ: C23/C2C22 ⊆ Aut C24964C24.27C2^3192,738
C24.28C23 = C2×C3⋊Q32φ: C23/C2C22 ⊆ Aut C24192C24.28C2^3192,739
C24.29C23 = Q16⋊D6φ: C23/C2C22 ⊆ Aut C24484+C24.29C2^3192,752
C24.30C23 = Q16.D6φ: C23/C2C22 ⊆ Aut C24964C24.30C2^3192,753
C24.31C23 = D8.9D6φ: C23/C2C22 ⊆ Aut C24964-C24.31C2^3192,754
C24.32C23 = C2×D83S3φ: C23/C2C22 ⊆ Aut C2496C24.32C2^3192,1315
C24.33C23 = C2×S3×Q16φ: C23/C2C22 ⊆ Aut C2496C24.33C2^3192,1322
C24.34C23 = C2×D24⋊C2φ: C23/C2C22 ⊆ Aut C2496C24.34C2^3192,1324
C24.35C23 = C2×D4.D6φ: C23/C2C22 ⊆ Aut C2496C24.35C2^3192,1319
C24.36C23 = SD1613D6φ: C23/C2C22 ⊆ Aut C24484C24.36C2^3192,1321
C24.37C23 = SD16⋊D6φ: C23/C2C22 ⊆ Aut C24484C24.37C2^3192,1327
C24.38C23 = D815D6φ: C23/C2C22 ⊆ Aut C24484+C24.38C2^3192,1328
C24.39C23 = D8.10D6φ: C23/C2C22 ⊆ Aut C24964-C24.39C2^3192,1330
C24.40C23 = D813D6φ: C23/C2C22 ⊆ Aut C24484C24.40C2^3192,1316
C24.41C23 = C2×Q16⋊S3φ: C23/C2C22 ⊆ Aut C2496C24.41C2^3192,1323
C24.42C23 = D12.30D4φ: C23/C2C22 ⊆ Aut C24964C24.42C2^3192,1325
C24.43C23 = D811D6φ: C23/C2C22 ⊆ Aut C24484C24.43C2^3192,1329
C24.44C23 = C2×Q8.7D6φ: C23/C2C22 ⊆ Aut C2496C24.44C2^3192,1320
C24.45C23 = S3×C4○D8φ: C23/C2C22 ⊆ Aut C24484C24.45C2^3192,1326
C24.46C23 = C6×C8.C22φ: C23/C2C22 ⊆ Aut C2496C24.46C2^3192,1463
C24.47C23 = C3×D8⋊C22φ: C23/C2C22 ⊆ Aut C24484C24.47C2^3192,1464
C24.48C23 = C3×D4○D8φ: C23/C2C22 ⊆ Aut C24484C24.48C2^3192,1465
C24.49C23 = C3×D4○SD16φ: C23/C2C22 ⊆ Aut C24484C24.49C2^3192,1466
C24.50C23 = C3×Q8○D8φ: C23/C2C22 ⊆ Aut C24964C24.50C2^3192,1467
C24.51C23 = C2×D12.C4φ: C23/C2C22 ⊆ Aut C2496C24.51C2^3192,1303
C24.52C23 = M4(2)⋊26D6φ: C23/C2C22 ⊆ Aut C24484C24.52C2^3192,1304
C24.53C23 = S3×C8○D4φ: C23/C2C22 ⊆ Aut C24484C24.53C2^3192,1308
C24.54C23 = M4(2)⋊28D6φ: C23/C2C22 ⊆ Aut C24484C24.54C2^3192,1309
C24.55C23 = C2×D48φ: C23/C22C2 ⊆ Aut C2496C24.55C2^3192,461
C24.56C23 = C2×C48⋊C2φ: C23/C22C2 ⊆ Aut C2496C24.56C2^3192,462
C24.57C23 = D487C2φ: C23/C22C2 ⊆ Aut C24962C24.57C2^3192,463
C24.58C23 = C2×Dic24φ: C23/C22C2 ⊆ Aut C24192C24.58C2^3192,464
C24.59C23 = C16⋊D6φ: C23/C22C2 ⊆ Aut C24484+C24.59C2^3192,467
C24.60C23 = C16.D6φ: C23/C22C2 ⊆ Aut C24964-C24.60C2^3192,468
C24.61C23 = C22×Dic12φ: C23/C22C2 ⊆ Aut C24192C24.61C2^3192,1301
C24.62C23 = C2×C4○D24φ: C23/C22C2 ⊆ Aut C2496C24.62C2^3192,1300
C24.63C23 = C6×D16φ: C23/C22C2 ⊆ Aut C2496C24.63C2^3192,938
C24.64C23 = C6×SD32φ: C23/C22C2 ⊆ Aut C2496C24.64C2^3192,939
C24.65C23 = C6×Q32φ: C23/C22C2 ⊆ Aut C24192C24.65C2^3192,940
C24.66C23 = C3×C4○D16φ: C23/C22C2 ⊆ Aut C24962C24.66C2^3192,941
C24.67C23 = C3×C16⋊C22φ: C23/C22C2 ⊆ Aut C24484C24.67C2^3192,942
C24.68C23 = C3×Q32⋊C2φ: C23/C22C2 ⊆ Aut C24964C24.68C2^3192,943
C24.69C23 = C2×C6×Q16φ: C23/C22C2 ⊆ Aut C24192C24.69C2^3192,1460
C24.70C23 = C6×C4○D8φ: C23/C22C2 ⊆ Aut C2496C24.70C2^3192,1461
C24.71C23 = S3×C2×C16φ: C23/C22C2 ⊆ Aut C2496C24.71C2^3192,458
C24.72C23 = C2×D6.C8φ: C23/C22C2 ⊆ Aut C2496C24.72C2^3192,459
C24.73C23 = D12.4C8φ: C23/C22C2 ⊆ Aut C24962C24.73C2^3192,460
C24.74C23 = S3×M5(2)φ: C23/C22C2 ⊆ Aut C24484C24.74C2^3192,465
C24.75C23 = C16.12D6φ: C23/C22C2 ⊆ Aut C24964C24.75C2^3192,466
C24.76C23 = C22×C3⋊C16φ: C23/C22C2 ⊆ Aut C24192C24.76C2^3192,655
C24.77C23 = C2×C12.C8φ: C23/C22C2 ⊆ Aut C2496C24.77C2^3192,656
C24.78C23 = C24.78C23φ: C23/C22C2 ⊆ Aut C24964C24.78C2^3192,699
C24.79C23 = C2×C8○D12φ: C23/C22C2 ⊆ Aut C2496C24.79C2^3192,1297
C24.80C23 = C6×C8○D4φ: C23/C22C2 ⊆ Aut C2496C24.80C2^3192,1456
C24.81C23 = C3×Q8○M4(2)φ: C23/C22C2 ⊆ Aut C24484C24.81C2^3192,1457
C24.82C23 = C6×M5(2)central extension (φ=1)96C24.82C2^3192,936
C24.83C23 = C3×D4○C16central extension (φ=1)962C24.83C2^3192,937

׿
×
𝔽