Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 3. #26018846 | C2 | semidirect |
| 4. #26018763 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018124 | C2 | semidirect |
| 10. #19151893 | C4 | semidirect |
| 11. #19151888 | C4 | semidirect |
| 12. #19151808 | C4 | semidirect |
| 13. #19151803 | C4 | semidirect |
| 202. C89 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030414 | 2 |
| #26029266 | 2 |
| #26018846 | 2 |
| #26018763 | 2 |
| #26018145 | 2 |
| #26018124 | 2 |
| C89×#1759 | 2 |
| #9159 | 89 |