Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
962 conjugacy classes of subgroups.
The subgroup lattice has 508 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21444445 | C2 | semidirect |
| 4. #21444422 | C2 | semidirect |
| 5. #21444420 | C2 | semidirect |
| 30. #16839503 | C22 | semidirect |
| 292. C61 | #17667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519769 | 2 |
| #21454452 | 2 |
| #21444445 | 2 |
| #21444422 | 2 |
| #21444420 | 2 |
| C61×#2920 | 2 |
| #17667 | 61 |