Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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. #21462057 | C2 | semidirect |
| 2. #21461704 | C2 | semidirect |
| 3. #21460794 | C2 | semidirect |
| 4. #21460793 | C2 | semidirect |
| 10. #16840659 | C22 | semidirect |
| 11. #16840631 | C22 | semidirect |
| 200. C61 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462057 | 2 |
| #21461704 | 2 |
| #21460794 | 2 |
| #21460793 | 2 |
| #21455465 | 2 |
| #11870 | 61 |