Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
526 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 121 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. #21434826 | C2 | semidirect |
| 2. #21433005 | C2 | semidirect |
| 3. #21426310 | C2 | semidirect |
| 4. #21426271 | C2 | semidirect |
| 5. #21426168 | C2 | semidirect |
| 6. #21426046 | C2 | semidirect |
| 8. #21425993 | C2 | semidirect |
| 9. #21425990 | C2 | semidirect |
| 10. #21425905 | C2 | semidirect |
| 11. C59×#2239 | C2 | semidirect |
| 17. #16837802 | C22 | semidirect |
| 18. #16837787 | C22 | semidirect |
| 26. #16837513 | C22 | semidirect |
| 27. #16837509 | C22 | semidirect |
| 31. #16837226 | C22 | semidirect |
| 32. #16837222 | C22 | semidirect |
| 33. #16837214 | C22 | semidirect |
| 37. #16837179 | C22 | semidirect |
| 40. C59×#365 | C22 | semidirect |
| 41. C59×#362 | C22 | semidirect |
| 196. #2239 | D59 | semidirect |
| 232. #365 | C2×D59 | semidirect |
| 234. #362 | C2×D59 | semidirect |
| 241. C59 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434826 | 2 |
| #21433005 | 2 |
| #21426310 | 2 |
| #21426271 | 2 |
| #21426168 | 2 |
| #21426046 | 2 |
| #21426044 | 2 |
| #21425993 | 2 |
| #21425990 | 2 |
| #21425905 | 2 |
| C59×#2239 | 2 |
| #33690 | 59 |