Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #26029323 | C2 | semidirect |
| 2. #26018887 | C2 | semidirect |
| 3. #26018799 | C2 | semidirect |
| 4. #26018799 | C2 | semidirect |
| 5. #26018124 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 20. #498×C89 | C4 | semidirect |
| 21. #493×C89 | C4 | semidirect |
| 22. #486×C89 | C4 | semidirect |
| 23. #486×C89 | C4 | semidirect |
| 175. C89 | #9417 | semidirect |
| 178. #498 | Dic89 | semidirect |
| 179. #493 | Dic89 | semidirect |
| 180. #486 | Dic89 | semidirect |
| 181. #486 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029323 | 2 |
| #26018887 | 2 |
| #26018799 | 2 |
| #26018124 | 2 |
| #26018117 | 2 |
| C89×#3184 | 2 |
| #9417 | 89 |