Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21456366 | C2 | semidirect |
| 3. #21444535 | C2 | semidirect |
| 5. #21444331 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 210. C61 | #10100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456366 | 2 |
| #21451759 | 2 |
| #21444535 | 2 |
| #21444417 | 2 |
| #21444331 | 2 |
| #21443711 | 2 |
| C61×#3215 | 2 |
| #10100 | 61 |