Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21448131 | C2 | semidirect |
| 2. C2×#16839597 | C2 | semidirect |
| 3. #21447939 | C2 | semidirect |
| 4. #21444009 | C2 | semidirect |
| 5. #21444003 | C2 | semidirect |
| 6. #21443961 | C2 | semidirect |
| 7. C61×#3415 | C2 | semidirect |
| 8. C2×D976 | C22 | semidirect |
| 13. #16839596 | C22 | semidirect |
| 14. C2×#14519683 | C22 | semidirect |
| 15. #16839592 | C22 | semidirect |
| 116. #3415 | D61 | semidirect |
| 146. C61 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448131 | 2 |
| C2×#16839597 | 2 |
| #21447939 | 2 |
| #21444009 | 2 |
| #21444003 | 2 |
| #21443961 | 2 |
| C61×#3415 | 2 |
| #13669 | 61 |