Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044306 | C2 | semidirect |
| 2. #26044287 | C2 | semidirect |
| 3. #26044285 | C2 | semidirect |
| 4. #26044283 | C2 | semidirect |
| 5. #26044280 | C2 | semidirect |
| 6. D8×D367 | C2 | semidirect |
| 7. #26044267 | C2 | semidirect |
| 8. C2×D8×C367 | C2 | semidirect |
| 10. #19154577 | C22 | semidirect |
| 12. #19154576 | C22 | semidirect |
| 15. D4×D367 | C22 | semidirect |
| 16. Dic1468 | C22 | semidirect |
| 17. #19154566 | C22 | semidirect |
| 18. #19154565 | C22 | semidirect |
| 19. D2936 | C22 | semidirect |
| 20. #19154562 | C22 | semidirect |
| 21. #19154561 | C22 | semidirect |
| 22. #19154560 | C22 | semidirect |
| 23. C8×D367 | C22 | semidirect |
| 24. C2×D4×C367 | C22 | semidirect |
| 25. D8×C367 | C22 | semidirect |
| 26. D8×C367 | C22 | semidirect |
| 27. C2×C8×C367 | C22 | semidirect |
| 62. C367 | #576 | semidirect |
| 70. C2×D8 | D367 | semidirect |
| 79. C2×D4 | C2×D367 | semidirect |
| 85. D8 | C2×D367 | semidirect |
| 86. D8 | C2×D367 | semidirect |
| 90. C2×C8 | C2×D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044306 | 2 |
| #26044287 | 2 |
| #26044285 | 2 |
| #26044283 | 2 |
| #26044280 | 2 |
| D8×D367 | 2 |
| #26044267 | 2 |
| C2×D8×C367 | 2 |
| #576 | 367 |