Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21425073 | C2 | semidirect |
| 4. #21422855 | C2 | semidirect |
| 5. #21422552 | C2 | semidirect |
| 7. C59×#1744 | C2 | semidirect |
| 10. #16837800 | C4 | semidirect |
| 11. #16837775 | C4 | semidirect |
| 12. #16837753 | C4 | semidirect |
| 13. #16837749 | C4 | semidirect |
| 163. #1744 | D59 | semidirect |
| 191. C59 | #9854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434655 | 2 |
| #21425073 | 2 |
| #21424924 | 2 |
| #21422855 | 2 |
| #21422552 | 2 |
| #21422548 | 2 |
| C59×#1744 | 2 |
| #9854 | 59 |