Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21435091 | C2 | semidirect |
| 2. #21434541 | C2 | semidirect |
| 3. #21423402 | C2 | semidirect |
| 4. #21423385 | C2 | semidirect |
| 5. #21422731 | C2 | semidirect |
| 6. #21422707 | C2 | semidirect |
| 7. C59×#3549 | C2 | semidirect |
| 9. #16837952 | C22 | semidirect |
| 10. #16837797 | C22 | semidirect |
| 12. #16837792 | C22 | semidirect |
| 13. #16837792 | C22 | semidirect |
| 15. #16837761 | C22 | semidirect |
| 19. #16837459 | C22 | semidirect |
| 20. C2×#14273638 | C22 | semidirect |
| 21. #16837142 | C22 | semidirect |
| 22. #16837142 | C22 | semidirect |
| 185. #3549 | D59 | semidirect |
| 222. C59 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435091 | 2 |
| #21434541 | 2 |
| #21423402 | 2 |
| #21423385 | 2 |
| #21422731 | 2 |
| #21422707 | 2 |
| C59×#3549 | 2 |
| #19052 | 59 |