Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26022064 | C2 | semidirect |
| 3. #26018229 | C2 | semidirect |
| 4. #26018226 | C2 | semidirect |
| 5. C89×#1453 | C2 | semidirect |
| 14. #19151419 | C22 | semidirect |
| 20. #322×C89 | C22 | semidirect |
| 21. C82×C89 | C22 | semidirect |
| 126. #1453 | D89 | semidirect |
| 129. C89 | #11670 | semidirect |
| 144. #322 | C2×D89 | semidirect |
| 145. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029163 | 2 |
| #26022064 | 2 |
| #26018229 | 2 |
| #26018226 | 2 |
| C89×#1453 | 2 |
| #11670 | 89 |