Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #26018785 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018129 | C2 | semidirect |
| 7. C89×#1472 | C2 | semidirect |
| 10. #19151933 | C4 | semidirect |
| 11. #19151916 | C4 | semidirect |
| 15. #19151754 | C4 | semidirect |
| 16. #19151737 | C4 | semidirect |
| 221. #1472 | D89 | semidirect |
| 224. C89 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031082 | 2 |
| #26029312 | 2 |
| #26018809 | 2 |
| #26018785 | 2 |
| #26018161 | 2 |
| #26018129 | 2 |
| C89×#1472 | 2 |
| #9331 | 89 |