Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021989 | C2 | semidirect |
| 3. #26020298 | C2 | semidirect |
| 4. #26018358 | C2 | semidirect |
| 5. C89×#3407 | C2 | semidirect |
| 8. #19151856 | C4 | semidirect |
| 9. #19151851 | C4 | semidirect |
| 50. M32×C89 | D4 | semidirect |
| 139. #3407 | D89 | semidirect |
| 144. C89 | #13077 | semidirect |
| 182. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029914 | 2 |
| #26021989 | 2 |
| #26020298 | 2 |
| #26018358 | 2 |
| C89×#3407 | 2 |
| #13077 | 89 |