Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029300 | C2 | semidirect |
| 3. #26020197 | C2 | semidirect |
| 4. #26020163 | C2 | semidirect |
| 5. #26018140 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1501 | C2 | semidirect |
| 11. #19151753 | C4 | semidirect |
| 12. #19151748 | C4 | semidirect |
| 14. #19151736 | C4 | semidirect |
| 15. #19151731 | C4 | semidirect |
| 294. #1501 | D89 | semidirect |
| 297. C89 | #9037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029468 | 2 |
| #26029300 | 2 |
| #26020197 | 2 |
| #26020163 | 2 |
| #26018140 | 2 |
| #26018100 | 2 |
| C89×#1501 | 2 |
| #9037 | 89 |