Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1270 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 231 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. #26028728 | C2 | semidirect |
| 3. #26020801 | C2 | semidirect |
| 4. #26020667 | C2 | semidirect |
| 5. #26020361 | C2 | semidirect |
| 6. #26020180 | C2 | semidirect |
| 7. C89×#1785 | C2 | semidirect |
| 19. C2×#15667931 | C22 | semidirect |
| 22. #19151562 | C22 | semidirect |
| 23. #19151370 | C22 | semidirect |
| 24. #19151369 | C22 | semidirect |
| 26. C2×#101×C89 | C22 | semidirect |
| 28. #407×C89 | C22 | semidirect |
| 200. #1785 | D89 | semidirect |
| 201. C89 | #21779 | semidirect |
| 215. C2×#101 | C2×D89 | semidirect |
| 220. #407 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033896 | 2 |
| #26028728 | 2 |
| #26020801 | 2 |
| #26020667 | 2 |
| #26020361 | 2 |
| #26020180 | 2 |
| C89×#1785 | 2 |
| #21779 | 89 |