Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
556 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21425671 | C2 | semidirect |
| 2. #21425271 | C2 | semidirect |
| 3. #21425267 | C2 | semidirect |
| 4. #21425071 | C2 | semidirect |
| 7. #21424339 | C2 | semidirect |
| 8. #21424333 | C2 | semidirect |
| 9. C59×#2102 | C2 | semidirect |
| 36. #14273727 | Q8 | semidirect |
| 38. #14273724 | Q8 | semidirect |
| 40. #14273715 | Q8 | semidirect |
| 153. #2102 | D59 | semidirect |
| 186. C59 | #32704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425671 | 2 |
| #21425271 | 2 |
| #21425267 | 2 |
| #21425071 | 2 |
| #21424923 | 2 |
| #21424478 | 2 |
| #21424339 | 2 |
| #21424333 | 2 |
| C59×#2102 | 2 |
| #32704 | 59 |