Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21434609 | C2 | semidirect |
| 3. #21426339 | C2 | semidirect |
| 4. #21426338 | C2 | semidirect |
| 5. #21426337 | C2 | semidirect |
| 6. #21426318 | C2 | semidirect |
| 7. #21425810 | C2 | semidirect |
| 8. #21425689 | C2 | semidirect |
| 9. C59×#2244 | C2 | semidirect |
| 15. #16837806 | C22 | semidirect |
| 16. #16837804 | C22 | semidirect |
| 26. #16837204 | C22 | semidirect |
| 27. #16837203 | C22 | semidirect |
| 28. #16837202 | C22 | semidirect |
| 29. #16837178 | C22 | semidirect |
| 30. C16×Dic59 | C22 | semidirect |
| 31. C59×#499 | C22 | semidirect |
| 33. C59×#357 | C22 | semidirect |
| 34. C59×#346 | C22 | semidirect |
| 156. #2244 | D59 | semidirect |
| 173. #499 | C2×D59 | semidirect |
| 186. #357 | C2×D59 | semidirect |
| 188. #346 | C2×D59 | semidirect |
| 190. C59 | #33704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434609 | 2 |
| #493×D59 | 2 |
| #21426339 | 2 |
| #21426338 | 2 |
| #21426337 | 2 |
| #21426318 | 2 |
| #21425810 | 2 |
| #21425689 | 2 |
| C59×#2244 | 2 |
| #33704 | 59 |