Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27133210 | C2 | semidirect |
| 2. #127×D191 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133008 | C2 | semidirect |
| 5. #27132859 | C2 | semidirect |
| 6. #27132858 | C2 | semidirect |
| 7. #27132855 | C2 | semidirect |
| 8. #27132798 | C2 | semidirect |
| 9. #27132795 | C2 | semidirect |
| 10. #27132715 | C2 | semidirect |
| 11. #459×C191 | C2 | semidirect |
| 16. C2×D1528 | C22 | semidirect |
| 17. C2×#15690272 | C22 | semidirect |
| 18. C2×#15690272 | C22 | semidirect |
| 19. #20259321 | C22 | semidirect |
| 24. #20259318 | C22 | semidirect |
| 29. C4×D764 | C22 | semidirect |
| 32. C4⋊(C191⋊C8) | C22 | semidirect |
| 33. #20259244 | C22 | semidirect |
| 34. #20259243 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 37. C8×Dic191 | C22 | semidirect |
| 38. C2×D8×C191 | C22 | semidirect |
| 40. C4×D4×C191 | C22 | semidirect |
| 41. C4⋊C8×C191 | C22 | semidirect |
| 42. #102×C191 | C22 | semidirect |
| 115. C4×D191 | D8 | semidirect |
| 165. C191 | #3205 | semidirect |
| 174. #459 | D191 | semidirect |
| 185. C2×D8 | C2×D191 | semidirect |
| 199. C4×D4 | C2×D191 | semidirect |
| 202. C4⋊C8 | C2×D191 | semidirect |
| 206. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133210 | 2 |
| #127×D191 | 2 |
| #27133038 | 2 |
| #27133008 | 2 |
| #27132859 | 2 |
| #27132858 | 2 |
| #27132855 | 2 |
| #27132798 | 2 |
| #27132795 | 2 |
| #27132715 | 2 |
| #459×C191 | 2 |
| #3205 | 191 |