Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #21448924 | C2 | semidirect |
| 3. #21444445 | C2 | semidirect |
| 5. #21443712 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 9. #16840130 | C4 | semidirect |
| 10. #16840126 | C4 | semidirect |
| 220. C61 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456219 | 2 |
| #21448924 | 2 |
| #21444445 | 2 |
| #21444327 | 2 |
| #21443712 | 2 |
| #21443711 | 2 |
| C61×#1505 | 2 |
| #9442 | 61 |