Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26021987 | C2 | semidirect |
| 3. #26021957 | C2 | semidirect |
| 4. #26021866 | C2 | semidirect |
| 5. C89×#1812 | C2 | semidirect |
| 11. #19152398 | C4 | semidirect |
| 14. C2×#15667952 | C22 | semidirect |
| 15. C22×#13083549 | C22 | semidirect |
| 21. #427×C89 | C22 | semidirect |
| 172. #1812 | D89 | semidirect |
| 173. C89 | #12745 | semidirect |
| 185. #427 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| #26021987 | 2 |
| #26021957 | 2 |
| #26021866 | 2 |
| C89×#1812 | 2 |
| #12745 | 89 |