Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 390 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. #26022523 | C2 | semidirect |
| 3. #26022297 | C2 | semidirect |
| 4. #26019742 | C2 | semidirect |
| 5. #26018294 | C2 | semidirect |
| 6. #26018211 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 14. #19151978 | C22 | semidirect |
| 21. C4⋊#13083549 | C22 | semidirect |
| 25. #346×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 178. #1333 | D89 | semidirect |
| 180. C89 | #12326 | semidirect |
| 197. #346 | C2×D89 | semidirect |
| 198. #334 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031862 | 2 |
| #26022523 | 2 |
| #26022297 | 2 |
| #26019742 | 2 |
| #26018294 | 2 |
| #26018211 | 2 |
| C89×#1333 | 2 |
| #12326 | 89 |