Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21432754 | C2 | semidirect |
| 5. #21422002 | C2 | semidirect |
| 6. #21421984 | C2 | semidirect |
| 7. C59×#1825 | C2 | semidirect |
| 16. #16837445 | C4 | semidirect |
| 17. #16837445 | C4 | semidirect |
| 19. #16837406 | C4 | semidirect |
| 20. #16837406 | C4 | semidirect |
| 217. #1825 | D59 | semidirect |
| 255. C59 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434036 | 2 |
| #21432754 | 2 |
| #21422663 | 2 |
| #21422455 | 2 |
| #21422002 | 2 |
| #21421984 | 2 |
| C59×#1825 | 2 |
| #9348 | 59 |