Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21446809 | C2 | semidirect |
| 2. #21444607 | C2 | semidirect |
| 4. #21444504 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 180. C61 | #10490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446809 | 2 |
| #21444607 | 2 |
| #21444554 | 2 |
| #21444504 | 2 |
| #21444236 | 2 |
| #21443710 | 2 |
| C61×#3226 | 2 |
| #10490 | 61 |