Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 582 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. #26018849 | C2 | semidirect |
| 3. #26018586 | C2 | semidirect |
| 4. #26018146 | C2 | semidirect |
| 5. C89×#2873 | C2 | semidirect |
| 61. #97×C89 | D4 | semidirect |
| 189. #2873 | D89 | semidirect |
| 194. C89 | #9387 | semidirect |
| 245. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025939 | 2 |
| #26018849 | 2 |
| #26018586 | 2 |
| #26018146 | 2 |
| C89×#2873 | 2 |
| #9387 | 89 |