Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #26029237 | C2 | semidirect |
| 3. #26018827 | C2 | semidirect |
| 4. #26018798 | C2 | semidirect |
| 5. #26018670 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 10. #19151992 | C4 | semidirect |
| 11. #19151987 | C4 | semidirect |
| 12. #19151967 | C4 | semidirect |
| 13. #19151963 | C4 | semidirect |
| 210. #1288 | D89 | semidirect |
| 212. C89 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031291 | 2 |
| #26029237 | 2 |
| #26018827 | 2 |
| #26018798 | 2 |
| #26018670 | 2 |
| #26018113 | 2 |
| C89×#1288 | 2 |
| #9370 | 89 |