Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26030201 | C2 | semidirect |
| 4. #26019279 | C2 | semidirect |
| 5. #26019245 | C2 | semidirect |
| 6. #26018786 | C2 | semidirect |
| 18. #19151934 | C22 | semidirect |
| 19. #19151929 | C22 | semidirect |
| 28. #19151336 | C22 | semidirect |
| 219. C89 | #18138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26030201 | 2 |
| #26024526 | 2 |
| #26019279 | 2 |
| #26019245 | 2 |
| #26018786 | 2 |
| C89×#1462 | 2 |
| #18138 | 89 |