Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #21454951 | C2 | semidirect |
| 2. #21444554 | C2 | semidirect |
| 3. #21444487 | C2 | semidirect |
| 4. #21444481 | C2 | semidirect |
| 8. #16839815 | C22 | semidirect |
| 9. #16839786 | C22 | semidirect |
| 10. #16839511 | C22 | semidirect |
| 11. #16839511 | C22 | semidirect |
| 12. #16839506 | C22 | semidirect |
| 13. #16839506 | C22 | semidirect |
| 137. C61 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454951 | 2 |
| #21444554 | 2 |
| #21444487 | 2 |
| #21444481 | 2 |
| C61×#3498 | 2 |
| #17782 | 61 |