Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #499×D59 | C2 | semidirect |
| 3. #21426343 | C2 | semidirect |
| 4. #21426342 | C2 | semidirect |
| 5. #21426337 | C2 | semidirect |
| 6. #21426326 | C2 | semidirect |
| 7. #21425805 | C2 | semidirect |
| 8. #21425689 | C2 | semidirect |
| 9. C59×#2244 | C2 | semidirect |
| 150. #2244 | D59 | semidirect |
| 183. C59 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D59 | 2 |
| #21434523 | 2 |
| #21426343 | 2 |
| #21426342 | 2 |
| #21426337 | 2 |
| #21426326 | 2 |
| #21425805 | 2 |
| #21425689 | 2 |
| C59×#2244 | 2 |
| #33708 | 59 |