Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #21422660 | C2 | semidirect |
| 5. #21421994 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C59×#1531 | C2 | semidirect |
| 9. #16837808 | C4 | semidirect |
| 10. #16837794 | C4 | semidirect |
| 11. #16837770 | C4 | semidirect |
| 12. #16837764 | C4 | semidirect |
| 195. #1531 | D59 | semidirect |
| 233. C59 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434799 | 2 |
| #21433090 | 2 |
| #21422660 | 2 |
| #21422635 | 2 |
| #21421994 | 2 |
| #21421978 | 2 |
| C59×#1531 | 2 |
| #9431 | 59 |