Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022064 | C2 | semidirect |
| 3. #26018292 | C2 | semidirect |
| 4. #26018290 | C2 | semidirect |
| 5. C89×#2165 | C2 | semidirect |
| 142. #2165 | D89 | semidirect |
| 145. C89 | #11993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030711 | 2 |
| #26022064 | 2 |
| #26018292 | 2 |
| #26018290 | 2 |
| C89×#2165 | 2 |
| #11993 | 89 |