Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19151636 | C2 | semidirect |
| 3. #26022461 | C2 | semidirect |
| 4. #26022444 | C2 | semidirect |
| 5. #26022040 | C2 | semidirect |
| 6. #26021965 | C2 | semidirect |
| 7. C89×#2112 | C2 | semidirect |
| 20. #19151426 | C22 | semidirect |
| 21. #19151424 | C22 | semidirect |
| 22. #19151403 | C22 | semidirect |
| 23. #19151400 | C22 | semidirect |
| 150. #2112 | D89 | semidirect |
| 151. C89 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029833 | 2 |
| C2×#19151636 | 2 |
| #26022461 | 2 |
| #26022444 | 2 |
| #26022040 | 2 |
| #26021965 | 2 |
| C89×#2112 | 2 |
| #33647 | 89 |