Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1328 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 279 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. #26028944 | C2 | semidirect |
| 3. #26020670 | C2 | semidirect |
| 4. #26020538 | C2 | semidirect |
| 5. #26020203 | C2 | semidirect |
| 6. #26020052 | C2 | semidirect |
| 7. C89×#3573 | C2 | semidirect |
| 8. C22×C8×D89 | C22 | semidirect |
| 14. #19151626 | C22 | semidirect |
| 18. #19151561 | C22 | semidirect |
| 19. #19151553 | C22 | semidirect |
| 20. #19151369 | C22 | semidirect |
| 57. C2×M16×C89 | D4 | semidirect |
| 60. C22×C8×C89 | D4 | semidirect |
| 145. #3573 | D89 | semidirect |
| 152. C89 | #21483 | semidirect |
| 185. C2×M16 | C22⋊D89 | semidirect |
| 191. C22×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029644 | 2 |
| #26028944 | 2 |
| #26020670 | 2 |
| #26020538 | 2 |
| #26020203 | 2 |
| #26020052 | 2 |
| C89×#3573 | 2 |
| #21483 | 89 |