Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
986 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 986 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 |
|---|---|---|
| 1. #26021947 | C2 | semidirect |
| 2. #26021927 | C2 | semidirect |
| 3. #26021893 | C2 | semidirect |
| 4. #26020222 | C2 | semidirect |
| 15. C22×#41×C89 | C4 | semidirect |
| 20. #536×C89 | C4 | semidirect |
| 23. #525×C89 | C4 | semidirect |
| 26. #518×C89 | C4 | semidirect |
| 235. C89 | #12713 | semidirect |
| 237. C22×#41 | Dic89 | semidirect |
| 242. #536 | Dic89 | semidirect |
| 245. #525 | Dic89 | semidirect |
| 248. #518 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021947 | 2 |
| #26021927 | 2 |
| #26021893 | 2 |
| #26020222 | 2 |
| C89×#3485 | 2 |
| #12713 | 89 |