Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21454842 | C2 | semidirect |
| 3. #21445826 | C2 | semidirect |
| 4. #21444378 | C2 | semidirect |
| 5. #21444219 | C2 | semidirect |
| 6. #21443714 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 12. #16839968 | C4 | semidirect |
| 13. #16839958 | C4 | semidirect |
| 194. #1286 | D61 | semidirect |
| 221. C61 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455285 | 2 |
| #21454842 | 2 |
| #21445826 | 2 |
| #21444378 | 2 |
| #21444219 | 2 |
| #21443714 | 2 |
| C61×#1286 | 2 |
| #9305 | 61 |