Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
352 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26022052 | C2 | semidirect |
| 3. #26020144 | C2 | semidirect |
| 4. #26018264 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 9. #19151999 | C4 | semidirect |
| 10. #19151983 | C4 | semidirect |
| 14. Q16×Dic89 | C4 | semidirect |
| 16. #19151680 | C4 | semidirect |
| 166. #1348 | D89 | semidirect |
| 169. C89 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030823 | 2 |
| #26022052 | 2 |
| #26020144 | 2 |
| #26018264 | 2 |
| #26018262 | 2 |
| #26018260 | 2 |
| C89×#1348 | 2 |
| #11746 | 89 |