Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
764 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018570 | C2 | semidirect |
| 3. #26018254 | C2 | semidirect |
| 4. C89×#1800 | C2 | semidirect |
| 14. #19151324 | C22 | semidirect |
| 19. #343×C89 | C22 | semidirect |
| 197. #1800 | D89 | semidirect |
| 200. C89 | #11880 | semidirect |
| 213. #343 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| #26018570 | 2 |
| #26018254 | 2 |
| C89×#1800 | 2 |
| #11880 | 89 |