Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26018273 | C2 | semidirect |
| 5. #26018252 | C2 | semidirect |
| 6. #26018182 | C2 | semidirect |
| 7. C89×#2764 | C2 | semidirect |
| 200. #2764 | D89 | semidirect |
| 207. C89 | #12193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021383 | 2 |
| #26019237 | 2 |
| #26019203 | 2 |
| #26018273 | 2 |
| #26018252 | 2 |
| #26018182 | 2 |
| C89×#2764 | 2 |
| #12193 | 89 |