Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26020062 | C2 | semidirect |
| 3. #26018843 | C2 | semidirect |
| 4. #26018761 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#2971 | C2 | semidirect |
| 10. #19151883 | C4 | semidirect |
| 11. #19151878 | C4 | semidirect |
| 12. #19151798 | C4 | semidirect |
| 13. #19151793 | C4 | semidirect |
| 204. #2971 | D89 | semidirect |
| 210. C89 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030403 | 2 |
| #26020062 | 2 |
| #26018843 | 2 |
| #26018761 | 2 |
| #26018146 | 2 |
| #26018125 | 2 |
| C89×#2971 | 2 |
| #9162 | 89 |