Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26022853 | C2 | semidirect |
| 3. #26020330 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 13. #19151501 | C4 | semidirect |
| 16. #19151467 | C4 | semidirect |
| 207. C89 | #9464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024724 | 2 |
| #26022853 | 2 |
| #26020330 | 2 |
| #26018781 | 2 |
| #26018106 | 2 |
| #26018104 | 2 |
| C89×#1510 | 2 |
| #9464 | 89 |