Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #21444578 | C2 | semidirect |
| 4. #21444509 | C2 | semidirect |
| 6. #21443693 | C2 | semidirect |
| 7. C61×#1493 | C2 | semidirect |
| 180. #1493 | D61 | semidirect |
| 210. C61 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455612 | 2 |
| #21445808 | 2 |
| #21444578 | 2 |
| #21444509 | 2 |
| C2×#16839491 | 2 |
| #21443693 | 2 |
| C61×#1493 | 2 |
| #10461 | 61 |