Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #21427016 | C2 | semidirect |
| 5. #21422492 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 13. #16837613 | C4 | semidirect |
| 14. #16837603 | C4 | semidirect |
| 201. #1303 | D59 | semidirect |
| 230. C59 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433570 | 2 |
| #21427016 | 2 |
| #21422657 | 2 |
| #21422590 | 2 |
| #21422492 | 2 |
| #21421956 | 2 |
| C59×#1303 | 2 |
| #9180 | 59 |