Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 76 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. #21462507 | C2 | semidirect |
| 2. #21461289 | C2 | semidirect |
| 3. #21461153 | C2 | semidirect |
| 4. #21461139 | C2 | semidirect |
| 5. #21460712 | C2 | semidirect |
| 6. #21460685 | C2 | semidirect |
| 229. C61 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462507 | 2 |
| #21461289 | 2 |
| #21461153 | 2 |
| #21461139 | 2 |
| #21460712 | 2 |
| #21460685 | 2 |
| #21455969 | 2 |
| #9313 | 61 |