Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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. #26028863 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. C2×#19151406 | C2 | semidirect |
| 5. C2×#504×C89 | C2 | semidirect |
| 14. C2×#15667948 | C22 | semidirect |
| 15. #19151406 | C22 | semidirect |
| 16. #19151406 | C22 | semidirect |
| 19. C2×M32×C89 | C22 | semidirect |
| 20. C22×C16×C89 | C22 | semidirect |
| 118. C2×#504 | D89 | semidirect |
| 122. C89 | #33385 | semidirect |
| 132. C2×M32 | C2×D89 | semidirect |
| 133. C22×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| #26028863 | 2 |
| #26021981 | 2 |
| C2×#19151406 | 2 |
| C2×#504×C89 | 2 |
| #33385 | 89 |