Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
374 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 374 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. #21444594 | C2 | semidirect |
| 4. #21444591 | C2 | semidirect |
| 6. #21443716 | C2 | semidirect |
| 7. C61×#1301 | C2 | semidirect |
| 162. #1301 | D61 | semidirect |
| 186. C61 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454456 | 2 |
| #21445800 | 2 |
| #21444594 | 2 |
| #21444591 | 2 |
| #21444131 | 2 |
| #21443716 | 2 |
| C61×#1301 | 2 |
| #8863 | 61 |