Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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. #26020003 | C2 | semidirect |
| 3. #26018868 | C2 | semidirect |
| 5. #26018765 | C2 | semidirect |
| 7. C89×#1568 | C2 | semidirect |
| 10. #19151996 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 179. #1568 | D89 | semidirect |
| 184. C89 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030811 | 2 |
| #26020003 | 2 |
| #26018868 | 2 |
| #26018864 | 2 |
| #26018765 | 2 |
| #26018761 | 2 |
| C89×#1568 | 2 |
| #9766 | 89 |