Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21454837 | C2 | semidirect |
| 3. #21445632 | C2 | semidirect |
| 4. #21444327 | C2 | semidirect |
| 5. #21443713 | C2 | semidirect |
| 6. #21443691 | C2 | semidirect |
| 7. C61×#1525 | C2 | semidirect |
| 10. #16840044 | C4 | semidirect |
| 11. #16840039 | C4 | semidirect |
| 12. #16839959 | C4 | semidirect |
| 13. #16839954 | C4 | semidirect |
| 200. #1525 | D61 | semidirect |
| 235. C61 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455964 | 2 |
| #21454837 | 2 |
| #21445632 | 2 |
| #21444327 | 2 |
| #21443713 | 2 |
| #21443691 | 2 |
| C61×#1525 | 2 |
| #9162 | 61 |