Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433201 | C2 | semidirect |
| 4. #21422648 | C2 | semidirect |
| 6. #21421961 | C2 | semidirect |
| 7. C59×#1291 | C2 | semidirect |
| 10. #16837807 | C4 | semidirect |
| 11. #16837775 | C4 | semidirect |
| 12. #16837753 | C4 | semidirect |
| 13. #16837749 | C4 | semidirect |
| 156. #1291 | D59 | semidirect |
| 182. C59 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434814 | 2 |
| #21433201 | 2 |
| #21422730 | 2 |
| #21422648 | 2 |
| #21422644 | 2 |
| #21421961 | 2 |
| C59×#1291 | 2 |
| #9418 | 59 |