Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
322 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 144 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. #92420⋊C16 | C2 | semidirect |
| 59. #92420 | M32 | semidirect |
| 92. C61 | #11402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462026 | 2 |
| C8×D61⋊C8 | 2 |
| #92420⋊C16 | 2 |
| #21447412 | 2 |
| #11402 | 61 |