Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020342 | C2 | semidirect |
| 3. #26020332 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 27. #483×C89 | C4 | semidirect |
| 29. #480×C89 | C4 | semidirect |
| 222. C89 | #9521 | semidirect |
| 226. #483 | Dic89 | semidirect |
| 228. #480 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029300 | 2 |
| #26020342 | 2 |
| #26020332 | 2 |
| #26018795 | 2 |
| #26018159 | 2 |
| #26018128 | 2 |
| C89×#3092 | 2 |
| #9521 | 89 |