Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1056 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26031380 | C2 | semidirect |
| 3. #26019395 | C2 | semidirect |
| 4. #26019366 | C2 | semidirect |
| 5. #26018914 | C2 | semidirect |
| 6. #26018670 | C2 | semidirect |
| 7. C89×#3152 | C2 | semidirect |
| 19. #19151885 | C22 | semidirect |
| 20. #19151651 | C22 | semidirect |
| 21. #19151347 | C22 | semidirect |
| 23. #19151327 | C22 | semidirect |
| 26. C2×C4⋊Q8×C89 | C22 | semidirect |
| 28. #494×C89 | C22 | semidirect |
| 30. C4×M16×C89 | C22 | semidirect |
| 174. #3152 | D89 | semidirect |
| 179. C89 | #18715 | semidirect |
| 190. C2×C4⋊Q8 | C2×D89 | semidirect |
| 193. #494 | C2×D89 | semidirect |
| 199. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26031380 | 2 |
| #26019395 | 2 |
| #26019366 | 2 |
| #26018914 | 2 |
| #26018670 | 2 |
| C89×#3152 | 2 |
| #18715 | 89 |