Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
772 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 772 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 |
|---|---|---|
| 1. #26029300 | C2 | semidirect |
| 2. #26020183 | C2 | semidirect |
| 3. #26020173 | C2 | semidirect |
| 4. #26018795 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 28. #450×C89 | C4 | semidirect |
| 30. #447×C89 | C4 | semidirect |
| 282. C89 | #9520 | semidirect |
| 287. #450 | Dic89 | semidirect |
| 289. #447 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029300 | 2 |
| #26020183 | 2 |
| #26020173 | 2 |
| #26018795 | 2 |
| #26018159 | 2 |
| #26018128 | 2 |
| C89×#3003 | 2 |
| #9520 | 89 |