Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26020401 | C2 | semidirect |
| 3. #26018247 | C2 | semidirect |
| 5. #26018241 | C2 | semidirect |
| 7. C89×#2165 | C2 | semidirect |
| 9. #19152000 | C4 | semidirect |
| 10. #19151982 | C4 | semidirect |
| 15. #19151711 | C4 | semidirect |
| 16. #19151706 | C4 | semidirect |
| 141. #2165 | D89 | semidirect |
| 147. C89 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030981 | 2 |
| #26020401 | 2 |
| #26018247 | 2 |
| #26018244 | 2 |
| #26018241 | 2 |
| #26018238 | 2 |
| C89×#2165 | 2 |
| #11836 | 89 |