Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
346 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022420 | C2 | semidirect |
| 3. #26019854 | C2 | semidirect |
| 4. #26018292 | C2 | semidirect |
| 5. #26018225 | C2 | semidirect |
| 6. #26018224 | C2 | semidirect |
| 7. C89×#2230 | C2 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 21. C8×#10623494 | C22 | semidirect |
| 22. #498×C89 | C22 | semidirect |
| 25. #364×C89 | C22 | semidirect |
| 168. #2230 | D89 | semidirect |
| 173. C89 | #12365 | semidirect |
| 176. #498 | C2×D89 | semidirect |
| 189. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032046 | 2 |
| #26022420 | 2 |
| #26019854 | 2 |
| #26018292 | 2 |
| #26018225 | 2 |
| #26018224 | 2 |
| C89×#2230 | 2 |
| #12365 | 89 |