Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26021861 | C2 | semidirect |
| 3. #26018178 | C2 | semidirect |
| 4. #26018177 | C2 | semidirect |
| 5. C89×#1315 | C2 | semidirect |
| 15. C22⋊#13083549 | C22 | semidirect |
| 18. C22⋊C16×C89 | C22 | semidirect |
| 179. #1315 | D89 | semidirect |
| 180. C89 | #11421 | semidirect |
| 193. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #408×D89 | 2 |
| #26021861 | 2 |
| #26018178 | 2 |
| #26018177 | 2 |
| C89×#1315 | 2 |
| #11421 | 89 |