Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
304 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425912 | C2 | semidirect |
| 2. #21423851 | C2 | semidirect |
| 3. #21422090 | C2 | semidirect |
| 5. #21422084 | C2 | semidirect |
| 17. C59×#498 | C4 | semidirect |
| 18. C59×#495 | C4 | semidirect |
| 23. C59×#442 | C4 | semidirect |
| 24. C59×#441 | C4 | semidirect |
| 153. #498 | Dic59 | semidirect |
| 154. #495 | Dic59 | semidirect |
| 159. #442 | Dic59 | semidirect |
| 160. #441 | Dic59 | semidirect |
| 171. C59 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425912 | 2 |
| #21423851 | 2 |
| #21422090 | 2 |
| #21422087 | 2 |
| #21422084 | 2 |
| #21422081 | 2 |
| C59×#3173 | 2 |
| #11769 | 59 |