Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 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. #21435107 | C2 | semidirect |
| 2. #21434441 | C2 | semidirect |
| 3. #21423402 | C2 | semidirect |
| 4. #21422731 | C2 | semidirect |
| 5. #21422707 | C2 | semidirect |
| 7. #16837959 | C22 | semidirect |
| 8. #16837797 | C22 | semidirect |
| 11. #16837761 | C22 | semidirect |
| 12. #16837761 | C22 | semidirect |
| 16. #16837459 | C22 | semidirect |
| 18. C2×#14273638 | C22 | semidirect |
| 19. #16837142 | C22 | semidirect |
| 20. #16837142 | C22 | semidirect |
| 200. C59 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435107 | 2 |
| #21434441 | 2 |
| #21423402 | 2 |
| #21422731 | 2 |
| #21422707 | 2 |
| C59×#3549 | 2 |
| #19056 | 59 |