Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26021845 | C2 | semidirect |
| 3. #26018997 | C2 | semidirect |
| 4. #26018220 | C2 | semidirect |
| 5. #26018219 | C2 | semidirect |
| 6. #26018218 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 20. #19151374 | C22 | semidirect |
| 23. #19151349 | C22 | semidirect |
| 25. #346×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 32. D8×D89 | C8 | semidirect |
| 173. #1333 | D89 | semidirect |
| 174. C89 | #11599 | semidirect |
| 189. #346 | C2×D89 | semidirect |
| 193. #334 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D89 | 2 |
| #26021845 | 2 |
| #26018997 | 2 |
| #26018220 | 2 |
| #26018219 | 2 |
| #26018218 | 2 |
| C89×#1333 | 2 |
| #11599 | 89 |