Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26023001 | C2 | semidirect |
| 5. #26018112 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1549 | C2 | semidirect |
| 9. #19151994 | C4 | semidirect |
| 10. #19151946 | C4 | semidirect |
| 185. #1549 | D89 | semidirect |
| 189. C89 | #9302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031380 | 2 |
| #26023001 | 2 |
| #26021083 | 2 |
| #26018813 | 2 |
| #26018112 | 2 |
| #26018080 | 2 |
| C89×#1549 | 2 |
| #9302 | 89 |