Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
888 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21456591 | C2 | semidirect |
| 3. #21446804 | C2 | semidirect |
| 5. #21444391 | C2 | semidirect |
| 6. #21443667 | C2 | semidirect |
| 271. C61 | #9955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456591 | 2 |
| C2×#16839913 | 2 |
| #21446804 | 2 |
| #21445750 | 2 |
| #21444391 | 2 |
| #21443667 | 2 |
| C61×#2435 | 2 |
| #9955 | 61 |