Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022048 | C2 | semidirect |
| 3. #26020381 | C2 | semidirect |
| 4. #26018265 | C2 | semidirect |
| 5. #26018263 | C2 | semidirect |
| 9. #19151999 | C4 | semidirect |
| 10. #19151981 | C4 | semidirect |
| 14. #19151692 | C4 | semidirect |
| 16. D8×Dic89 | C4 | semidirect |
| 167. C89 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030817 | 2 |
| #26022048 | 2 |
| #26020381 | 2 |
| #26018265 | 2 |
| #26018263 | 2 |
| #26018261 | 2 |
| C89×#1347 | 2 |
| #11855 | 89 |