Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022134 | C2 | semidirect |
| 3. #26018455 | C2 | semidirect |
| 4. #26018436 | C2 | semidirect |
| 5. #26018435 | C2 | semidirect |
| 6. #26018386 | C2 | semidirect |
| 7. C89×#2178 | C2 | semidirect |
| 10. #19151438 | C4 | semidirect |
| 11. #19151436 | C4 | semidirect |
| 12. #19151435 | C4 | semidirect |
| 13. #19151433 | C4 | semidirect |
| 94. #2178 | D89 | semidirect |
| 99. C89 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022559 | 2 |
| #26022134 | 2 |
| #26018455 | 2 |
| #26018436 | 2 |
| #26018435 | 2 |
| #26018386 | 2 |
| C89×#2178 | 2 |
| #13656 | 89 |