Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #26018725 | C2 | semidirect |
| 5. #26018596 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 7. C89×#3113 | C2 | semidirect |
| 187. #3113 | D89 | semidirect |
| 193. C89 | #10044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031450 | 2 |
| #26030283 | 2 |
| #26018886 | 2 |
| #26018725 | 2 |
| #26018596 | 2 |
| #26018113 | 2 |
| C89×#3113 | 2 |
| #10044 | 89 |