Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26022054 | C2 | semidirect |
| 3. #334×D89 | C2 | semidirect |
| 4. #26018304 | C2 | semidirect |
| 5. #26018296 | C2 | semidirect |
| 6. #26018294 | C2 | semidirect |
| 7. C89×#1363 | C2 | semidirect |
| 154. #1363 | D89 | semidirect |
| 157. C89 | #11945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030824 | 2 |
| #26022054 | 2 |
| #334×D89 | 2 |
| #26018304 | 2 |
| #26018296 | 2 |
| #26018294 | 2 |
| C89×#1363 | 2 |
| #11945 | 89 |