Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 358 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 |
|---|---|---|
| 32. #14519712 | C8 | semidirect |
| 120. C61 | #8294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461368 | 2 |
| M16×#92420 | 2 |
| C2×#16840603 | 2 |
| #21460652 | 2 |
| #21445720 | 2 |
| #8294 | 61 |