Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #21422517 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421959 | C2 | semidirect |
| 7. C59×#1515 | C2 | semidirect |
| 9. #16837808 | C4 | semidirect |
| 10. #16837808 | C4 | semidirect |
| 11. #16837764 | C4 | semidirect |
| 12. #16837764 | C4 | semidirect |
| 188. #1515 | D59 | semidirect |
| 224. C59 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435336 | 2 |
| #21433076 | 2 |
| #21422671 | 2 |
| #21422517 | 2 |
| #21421960 | 2 |
| #21421959 | 2 |
| C59×#1515 | 2 |
| #9369 | 59 |