Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #21422711 | C2 | semidirect |
| 5. #21421996 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1503 | C2 | semidirect |
| 10. #16837679 | C4 | semidirect |
| 11. #16837679 | C4 | semidirect |
| 12. #16837604 | C4 | semidirect |
| 13. #16837604 | C4 | semidirect |
| 208. #1503 | D59 | semidirect |
| 243. C59 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434191 | 2 |
| #21433130 | 2 |
| #21423924 | 2 |
| #21422711 | 2 |
| #21421996 | 2 |
| #21421952 | 2 |
| C59×#1503 | 2 |
| #9165 | 59 |