Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21444240 | C2 | semidirect |
| 5. #21443718 | C2 | semidirect |
| 6. #21443692 | C2 | semidirect |
| 7. C61×#1531 | C2 | semidirect |
| 179. #1531 | D61 | semidirect |
| 212. C61 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455975 | 2 |
| #21454468 | 2 |
| #21444251 | 2 |
| #21444240 | 2 |
| #21443718 | 2 |
| #21443692 | 2 |
| C61×#1531 | 2 |
| #9314 | 61 |