Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
430 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #26021201 | C2 | semidirect |
| 3. #26018969 | C2 | semidirect |
| 5. #26018121 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 26. #497×C89 | C4 | semidirect |
| 27. #491×C89 | C4 | semidirect |
| 197. C89 | #9376 | semidirect |
| 200. #497 | Dic89 | semidirect |
| 201. #491 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029391 | 2 |
| #26021201 | 2 |
| #26018969 | 2 |
| #26018777 | 2 |
| #26018121 | 2 |
| #26018107 | 2 |
| C89×#3218 | 2 |
| #9376 | 89 |