Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #26018890 | C2 | semidirect |
| 3. #26018803 | C2 | semidirect |
| 5. #26018124 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 20. #500×C89 | C4 | semidirect |
| 21. #492×C89 | C4 | semidirect |
| 22. #487×C89 | C4 | semidirect |
| 23. #486×C89 | C4 | semidirect |
| 167. C89 | #9415 | semidirect |
| 170. #500 | Dic89 | semidirect |
| 171. #492 | Dic89 | semidirect |
| 172. #487 | Dic89 | semidirect |
| 173. #486 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029323 | 2 |
| #26018890 | 2 |
| #26018803 | 2 |
| #26018799 | 2 |
| #26018124 | 2 |
| #26018117 | 2 |
| C89×#3182 | 2 |
| #9415 | 89 |