Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21444505 | C2 | semidirect |
| 4. #21444503 | C2 | semidirect |
| 6. #21443677 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 188. #1286 | D61 | semidirect |
| 216. C61 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454456 | 2 |
| #21451643 | 2 |
| #21444505 | 2 |
| #21444503 | 2 |
| #21444131 | 2 |
| #21443677 | 2 |
| C61×#1286 | 2 |
| #9194 | 61 |