Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 98 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. #21461930 | C2 | semidirect |
| 4. #21461612 | C2 | semidirect |
| 5. #21460698 | C2 | semidirect |
| 6. #21460648 | C2 | semidirect |
| 23. #16839506 | C4 | semidirect |
| 24. #16839505 | C4 | semidirect |
| 25. #16839505 | C4 | semidirect |
| 26. C61×#331 | C4 | semidirect |
| 243. #331 | #6923 | semidirect |
| 244. C61 | #9563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461986 | 2 |
| #21461947 | 2 |
| #21461930 | 2 |
| #21461612 | 2 |
| #21460698 | 2 |
| #21460648 | 2 |
| #331×D61 | 2 |
| #9563 | 61 |