Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022489 | C2 | semidirect |
| 3. #26022399 | C2 | semidirect |
| 4. #26019766 | C2 | semidirect |
| 5. #26018294 | C2 | semidirect |
| 6. #26018211 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 10. #19152003 | C22 | semidirect |
| 19. C4⋊#13083549 | C22 | semidirect |
| 25. #346×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 99. D8×C89 | SD16 | semidirect |
| 172. #1333 | D89 | semidirect |
| 174. C89 | #12378 | semidirect |
| 191. #346 | C2×D89 | semidirect |
| 192. #334 | C2×D89 | semidirect |
| 253. D8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031862 | 2 |
| #26022489 | 2 |
| #26022399 | 2 |
| #26019766 | 2 |
| #26018294 | 2 |
| #26018211 | 2 |
| C89×#1333 | 2 |
| #12378 | 89 |