Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26029327 | C2 | semidirect |
| 3. #26018759 | C2 | semidirect |
| 4. #26018759 | C2 | semidirect |
| 5. #26018722 | C2 | semidirect |
| 6. #26018114 | C2 | semidirect |
| 7. C89×#1274 | C2 | semidirect |
| 10. #19151975 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 185. #1274 | D89 | semidirect |
| 186. C89 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031187 | 2 |
| #26029327 | 2 |
| #26018759 | 2 |
| #26018722 | 2 |
| #26018114 | 2 |
| C89×#1274 | 2 |
| #9281 | 89 |