Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21454879 | C2 | semidirect |
| 3. #21444376 | C2 | semidirect |
| 4. #21444348 | C2 | semidirect |
| 5. #21443728 | C2 | semidirect |
| 6. #21443696 | C2 | semidirect |
| 7. C61×#1471 | C2 | semidirect |
| 9. #16840092 | C4 | semidirect |
| 11. #16840075 | C4 | semidirect |
| 14. #16839913 | C4 | semidirect |
| 16. #16839896 | C4 | semidirect |
| 222. #1471 | D61 | semidirect |
| 260. C61 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456633 | 2 |
| #21454879 | 2 |
| #21444376 | 2 |
| #21444348 | 2 |
| #21443728 | 2 |
| #21443696 | 2 |
| C61×#1471 | 2 |
| #9332 | 61 |