Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #26034666 | C2 | semidirect |
| 2. #26031195 | C2 | semidirect |
| 4. #26019331 | C2 | semidirect |
| 5. #26019312 | C2 | semidirect |
| 6. #26018672 | C2 | semidirect |
| 7. C89×#1543 | C2 | semidirect |
| 10. #19152334 | C22 | semidirect |
| 11. #19152328 | C22 | semidirect |
| 26. #19151328 | C22 | semidirect |
| 29. #333×C89 | C22 | semidirect |
| 30. #331×C89 | C22 | semidirect |
| 173. #1543 | D89 | semidirect |
| 175. C89 | #18718 | semidirect |
| 196. #333 | C2×D89 | semidirect |
| 197. #331 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034666 | 2 |
| #26031195 | 2 |
| #26030705 | 2 |
| #26019331 | 2 |
| #26019312 | 2 |
| #26018672 | 2 |
| C89×#1543 | 2 |
| #18718 | 89 |