Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022061 | C2 | semidirect |
| 3. #26020402 | C2 | semidirect |
| 4. #26018242 | C2 | semidirect |
| 5. #26018238 | C2 | semidirect |
| 6. #26018237 | C2 | semidirect |
| 7. C89×#1341 | C2 | semidirect |
| 9. #19151995 | C4 | semidirect |
| 10. #19151973 | C4 | semidirect |
| 14. #19151710 | C4 | semidirect |
| 15. #19151709 | C4 | semidirect |
| 153. #1341 | D89 | semidirect |
| 156. C89 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030985 | 2 |
| #26022061 | 2 |
| #26020402 | 2 |
| #26018242 | 2 |
| #26018238 | 2 |
| #26018237 | 2 |
| C89×#1341 | 2 |
| #11837 | 89 |