Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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. #26018556 | C2 | semidirect |
| 3. #26018554 | C2 | semidirect |
| 4. #26018553 | C2 | semidirect |
| 5. #26018552 | C2 | semidirect |
| 6. #26018551 | C2 | semidirect |
| 7. C89×#1454 | C2 | semidirect |
| 18. #19151320 | C22 | semidirect |
| 19. #19151320 | C22 | semidirect |
| 20. #19151319 | C22 | semidirect |
| 21. C8×#10623494 | C22 | semidirect |
| 23. #322×C89 | C22 | semidirect |
| 24. C82×C89 | C22 | semidirect |
| 105. #1454 | D89 | semidirect |
| 106. C89 | #17339 | semidirect |
| 121. #322 | C2×D89 | semidirect |
| 123. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028880 | 2 |
| #26018556 | 2 |
| #26018554 | 2 |
| #26018553 | 2 |
| #26018552 | 2 |
| #26018551 | 2 |
| C89×#1454 | 2 |
| #17339 | 89 |