Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21425761 | C2 | semidirect |
| 2. #21422688 | C2 | semidirect |
| 3. #21422247 | C2 | semidirect |
| 7. #16837197 | C22 | semidirect |
| 10. #16837142 | C22 | semidirect |
| 11. C59×#585 | C4 | semidirect |
| 14. C59×#456 | C4 | semidirect |
| 19. C59×#413 | C4 | semidirect |
| 179. #585 | Dic59 | semidirect |
| 182. #456 | Dic59 | semidirect |
| 187. #413 | Dic59 | semidirect |
| 194. C59 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425761 | 2 |
| #21422688 | 2 |
| #21422247 | 2 |
| C59×#3018 | 2 |
| #13568 | 59 |