Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022519 | C2 | semidirect |
| 2. #26022287 | C2 | semidirect |
| 3. #26019731 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018219 | C2 | semidirect |
| 6. #26018210 | C2 | semidirect |
| 7. C89×#3273 | C2 | semidirect |
| 11. #19151975 | C22 | semidirect |
| 13. C4⋊#13083549 | C22 | semidirect |
| 15. #19151374 | C22 | semidirect |
| 16. #19151349 | C22 | semidirect |
| 98. D8×C89 | D8 | semidirect |
| 180. #3273 | D89 | semidirect |
| 187. C89 | #12324 | semidirect |
| 275. D8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022519 | 2 |
| #26022287 | 2 |
| #26019731 | 2 |
| #26018295 | 2 |
| #26018219 | 2 |
| #26018210 | 2 |
| C89×#3273 | 2 |
| #12324 | 89 |