Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
850 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26031454 | C2 | semidirect |
| 3. #26019585 | C2 | semidirect |
| 5. #26018853 | C2 | semidirect |
| 15. #19152004 | C22 | semidirect |
| 16. #19151966 | C22 | semidirect |
| 21. #19151339 | C22 | semidirect |
| 169. C89 | #18999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152348 | 2 |
| #26031454 | 2 |
| #26019585 | 2 |
| #26018876 | 2 |
| #26018853 | 2 |
| C89×#3140 | 2 |
| #18999 | 89 |