Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 492 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. #26021196 | C2 | semidirect |
| 4. #26018765 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 10. #19151878 | C4 | semidirect |
| 11. #19151803 | C4 | semidirect |
| 189. C89 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030351 | 2 |
| #26022895 | 2 |
| #26021196 | 2 |
| #26018765 | 2 |
| #26018146 | 2 |
| #26018107 | 2 |
| C89×#1490 | 2 |
| #9327 | 89 |