Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21447986 | C2 | semidirect |
| 3. #21447981 | C2 | semidirect |
| 6. #21447868 | C2 | semidirect |
| 7. #21447867 | C2 | semidirect |
| 172. C61 | #33827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456471 | 2 |
| #21447986 | 2 |
| #21447981 | 2 |
| #21447927 | 2 |
| #21447908 | 2 |
| #21447868 | 2 |
| #21447867 | 2 |
| #21447579 | 2 |
| C61×#2219 | 2 |
| #33827 | 61 |