Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26022054 | C2 | semidirect |
| 3. #26022049 | C2 | semidirect |
| 4. #26018208 | C2 | semidirect |
| 5. D4⋊#13083549 | C2 | semidirect |
| 6. #26018206 | C2 | semidirect |
| 7. C89×D4⋊C16 | C2 | semidirect |
| 18. C4⋊#13083549 | C22 | semidirect |
| 23. C4×#13083549 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 26. C4×C16×C89 | C22 | semidirect |
| 181. D4⋊C16 | D89 | semidirect |
| 182. C89 | #11631 | semidirect |
| 196. C4⋊C16 | C2×D89 | semidirect |
| 201. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×D89 | 2 |
| #26022054 | 2 |
| #26022049 | 2 |
| #26018208 | 2 |
| D4⋊#13083549 | 2 |
| #26018206 | 2 |
| C89×D4⋊C16 | 2 |
| #11631 | 89 |