Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #26029312 | C2 | semidirect |
| 3. #26018806 | C2 | semidirect |
| 4. #26018612 | C2 | semidirect |
| 5. #26018160 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#1510 | C2 | semidirect |
| 9. #19151928 | C4 | semidirect |
| 11. #19151911 | C4 | semidirect |
| 14. #19151749 | C4 | semidirect |
| 16. #19151732 | C4 | semidirect |
| 229. #1510 | D89 | semidirect |
| 233. C89 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031066 | 2 |
| #26029312 | 2 |
| #26018806 | 2 |
| #26018612 | 2 |
| #26018160 | 2 |
| #26018128 | 2 |
| C89×#1510 | 2 |
| #9332 | 89 |