Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
290 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×#16840695 | C2 | semidirect |
| 2. D61⋊M64 | C2 | semidirect |
| 3. #21460937 | C2 | semidirect |
| 4. #21460936 | C2 | semidirect |
| 9. #16840694 | C22 | semidirect |
| 11. C2×#14519827 | C22 | semidirect |
| 160. C61 | #13558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840695 | 2 |
| D61⋊M64 | 2 |
| #21460937 | 2 |
| #21460936 | 2 |
| #504×D61 | 2 |
| #13558 | 61 |