Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
992 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26031259 | C2 | semidirect |
| 3. #26019557 | C2 | semidirect |
| 4. #26018887 | C2 | semidirect |
| 5. #26018862 | C2 | semidirect |
| 6. C89×#3135 | C2 | semidirect |
| 15. #19151990 | C22 | semidirect |
| 16. #19151960 | C22 | semidirect |
| 20. #19151655 | C22 | semidirect |
| 21. #19151338 | C22 | semidirect |
| 22. #19151337 | C22 | semidirect |
| 23. #533×C89 | C22 | semidirect |
| 27. #489×C89 | C22 | semidirect |
| 29. C2×#97×C89 | C22 | semidirect |
| 173. #3135 | D89 | semidirect |
| 177. C89 | #19056 | semidirect |
| 185. #533 | C2×D89 | semidirect |
| 192. #489 | C2×D89 | semidirect |
| 198. C2×#97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26031259 | 2 |
| #26019557 | 2 |
| #26018887 | 2 |
| #26018862 | 2 |
| C89×#3135 | 2 |
| #19056 | 89 |