Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022401 | C2 | semidirect |
| 3. #26019648 | C2 | semidirect |
| 4. #26018298 | C2 | semidirect |
| 5. #26018217 | C2 | semidirect |
| 6. #26018208 | C2 | semidirect |
| 7. C89×#2240 | C2 | semidirect |
| 141. #2240 | D89 | semidirect |
| 147. C89 | #12373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032010 | 2 |
| #26022401 | 2 |
| #26019648 | 2 |
| #26018298 | 2 |
| #26018217 | 2 |
| #26018208 | 2 |
| C89×#2240 | 2 |
| #12373 | 89 |