Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21456366 | C2 | semidirect |
| 4. #21446663 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1485 | C2 | semidirect |
| 180. #1485 | D61 | semidirect |
| 210. C61 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457202 | 2 |
| #21456949 | 2 |
| #21456366 | 2 |
| #21446663 | 2 |
| #21444410 | 2 |
| #21443710 | 2 |
| C61×#1485 | 2 |
| #10116 | 61 |