Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022466 | C2 | semidirect |
| 3. #26021826 | C2 | semidirect |
| 4. #26018238 | C2 | semidirect |
| 5. #26018237 | C2 | semidirect |
| 6. #26018202 | C2 | semidirect |
| 7. C89×#2238 | C2 | semidirect |
| 149. #2238 | D89 | semidirect |
| 154. C89 | #12307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031629 | 2 |
| #26022466 | 2 |
| #26021826 | 2 |
| #26018238 | 2 |
| #26018237 | 2 |
| #26018202 | 2 |
| C89×#2238 | 2 |
| #12307 | 89 |