Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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 |
|---|---|---|
| 2. #21433085 | C2 | semidirect |
| 3. #21422707 | C2 | semidirect |
| 4. #21422632 | C2 | semidirect |
| 5. #21421996 | C2 | semidirect |
| 6. #21421977 | C2 | semidirect |
| 7. C59×#1517 | C2 | semidirect |
| 9. #16837808 | C4 | semidirect |
| 10. #16837789 | C4 | semidirect |
| 11. #16837766 | C4 | semidirect |
| 12. #16837764 | C4 | semidirect |
| 205. #1517 | D59 | semidirect |
| 243. C59 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434788 | 2 |
| #21433085 | 2 |
| #21422707 | 2 |
| #21422632 | 2 |
| #21421996 | 2 |
| #21421977 | 2 |
| C59×#1517 | 2 |
| #9432 | 59 |