Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 9. #19151998 | C4 | semidirect |
| 10. #19151976 | C4 | semidirect |
| 14. #19151705 | C4 | semidirect |
| 15. #19151704 | C4 | semidirect |
| 146. C89 | #11771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030906 | 2 |
| #26022065 | 2 |
| #26020006 | 2 |
| #26018247 | 2 |
| #26018246 | 2 |
| #26018239 | 2 |
| C89×#1340 | 2 |
| #11771 | 89 |