Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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. #21422607 | C2 | semidirect |
| 5. #21422570 | C2 | semidirect |
| 6. #21421958 | C2 | semidirect |
| 7. C59×#1274 | C2 | semidirect |
| 10. #16837807 | C4 | semidirect |
| 11. #16837800 | C4 | semidirect |
| 12. #16837749 | C4 | semidirect |
| 13. #16837749 | C4 | semidirect |
| 170. #1274 | D59 | semidirect |
| 197. C59 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435234 | 2 |
| #21433171 | 2 |
| #21422607 | 2 |
| #21422603 | 2 |
| #21422570 | 2 |
| #21421958 | 2 |
| C59×#1274 | 2 |
| #9279 | 59 |