Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26022169 | C2 | semidirect |
| 3. #26021371 | C2 | semidirect |
| 4. #26018268 | C2 | semidirect |
| 5. #26018267 | C2 | semidirect |
| 6. #26018177 | C2 | semidirect |
| 7. C89×#2185 | C2 | semidirect |
| 20. C22⋊#13083549 | C22 | semidirect |
| 21. #19151363 | C22 | semidirect |
| 22. C22×Q16×C89 | C22 | semidirect |
| 26. C22⋊C16×C89 | C22 | semidirect |
| 187. #2185 | D89 | semidirect |
| 192. C89 | #12111 | semidirect |
| 194. C22×Q16 | C2×D89 | semidirect |
| 210. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031112 | 2 |
| #26022169 | 2 |
| #26021371 | 2 |
| #26018268 | 2 |
| #26018267 | 2 |
| #26018177 | 2 |
| C89×#2185 | 2 |
| #12111 | 89 |