Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26031861 | C2 | semidirect |
| 2. #26022519 | C2 | semidirect |
| 3. #26022288 | C2 | semidirect |
| 4. #26019732 | C2 | semidirect |
| 5. #26018218 | C2 | semidirect |
| 6. #26018209 | C2 | semidirect |
| 7. C89×#1360 | C2 | semidirect |
| 13. #19151975 | C22 | semidirect |
| 22. #19151374 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 88. D712 | D8 | semidirect |
| 184. #1360 | D89 | semidirect |
| 187. C89 | #12324 | semidirect |
| 202. C4⋊C16 | C2×D89 | semidirect |
| 205. #334 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031861 | 2 |
| #26022519 | 2 |
| #26022288 | 2 |
| #26019732 | 2 |
| #26018218 | 2 |
| #26018209 | 2 |
| C89×#1360 | 2 |
| #12324 | 89 |