Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #21456366 | C2 | semidirect |
| 4. #21444535 | C2 | semidirect |
| 6. #21443712 | C2 | semidirect |
| 7. C61×#1506 | C2 | semidirect |
| 185. #1506 | D61 | semidirect |
| 215. C61 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456818 | 2 |
| #21456366 | 2 |
| #21451929 | 2 |
| #21444535 | 2 |
| #21444418 | 2 |
| #21443712 | 2 |
| C61×#1506 | 2 |
| #10102 | 61 |