Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
742 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433354 | C2 | semidirect |
| 3. #21424007 | C2 | semidirect |
| 4. #21422460 | C2 | semidirect |
| 5. #21422456 | C2 | semidirect |
| 6. #21421973 | C2 | semidirect |
| 7. C59×#3187 | C2 | semidirect |
| 239. #3187 | D59 | semidirect |
| 279. C59 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433354 | 2 |
| #21433346 | 2 |
| #21424007 | 2 |
| #21422460 | 2 |
| #21422456 | 2 |
| #21421973 | 2 |
| C59×#3187 | 2 |
| #9975 | 59 |