Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019162 | C2 | semidirect |
| 3. #26018317 | C2 | semidirect |
| 4. #26018221 | C2 | semidirect |
| 6. #26018173 | C2 | semidirect |
| 53. #13083549 | M16 | semidirect |
| 110. C89 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022116 | 2 |
| #26019162 | 2 |
| #26018317 | 2 |
| #26018221 | 2 |
| #26018219 | 2 |
| #26018173 | 2 |
| C89×#1594 | 2 |
| #12087 | 89 |