Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023418 | C2 | semidirect |
| 4. #26018772 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 25. #484×C89 | C4 | semidirect |
| 28. #450×C89 | C4 | semidirect |
| 236. C89 | #9344 | semidirect |
| 239. #484 | Dic89 | semidirect |
| 242. #450 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023418 | 2 |
| #26021089 | 2 |
| #26018781 | 2 |
| #26018772 | 2 |
| #26018159 | 2 |
| #26018106 | 2 |
| C89×#3193 | 2 |
| #9344 | 89 |