Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D59 | C2 | semidirect |
| 3. #21426339 | C2 | semidirect |
| 4. #21426338 | C2 | semidirect |
| 5. #21426337 | C2 | semidirect |
| 6. #21426336 | C2 | semidirect |
| 7. #357×D59 | C2 | semidirect |
| 8. #346×D59 | C2 | semidirect |
| 9. C59×#2244 | C2 | semidirect |
| 15. #16837804 | C22 | semidirect |
| 16. #16837803 | C22 | semidirect |
| 26. #16837204 | C22 | semidirect |
| 27. #16837203 | C22 | semidirect |
| 28. #16837202 | C22 | semidirect |
| 29. #16837178 | C22 | semidirect |
| 30. #16837177 | C22 | semidirect |
| 31. C59×#499 | C22 | semidirect |
| 33. C59×#357 | C22 | semidirect |
| 34. C59×#346 | C22 | semidirect |
| 157. #2244 | D59 | direct (N × H) |
| 164. D59 | #2244 | direct (N × H) |
| 174. #499 | C2×D59 | semidirect |
| 186. #357 | C2×D59 | semidirect |
| 189. #346 | C2×D59 | semidirect |
| 190. C59 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D59 | 2 |
| #493×D59 | 2 |
| #21426339 | 2 |
| #21426338 | 2 |
| #21426337 | 2 |
| #21426336 | 2 |
| #357×D59 | 2 |
| #346×D59 | 2 |
| C59×#2244 | 2 |
| C2×#2244 | 59 |