Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 74 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. #21461311 | C2 | semidirect |
| 4. #21461128 | C2 | semidirect |
| 5. #21460683 | C2 | semidirect |
| 6. #21460675 | C2 | semidirect |
| 243. C61 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462710 | 2 |
| #21461339 | 2 |
| #21461311 | 2 |
| #21461128 | 2 |
| #21460683 | 2 |
| #21460675 | 2 |
| #21456831 | 2 |
| #9373 | 61 |