Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21446796 | C2 | semidirect |
| 5. #21444239 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1276 | C2 | semidirect |
| 11. #16840048 | C4 | semidirect |
| 12. #16840043 | C4 | semidirect |
| 13. #16839973 | C4 | semidirect |
| 14. #16839968 | C4 | semidirect |
| 207. #1276 | D61 | semidirect |
| 238. C61 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455891 | 2 |
| #21454948 | 2 |
| #21446796 | 2 |
| C4×#14519705 | 2 |
| #21444239 | 2 |
| #21443710 | 2 |
| C61×#1276 | 2 |
| #8972 | 61 |