Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021981 | C2 | semidirect |
| 3. #26020302 | C2 | semidirect |
| 4. #26018351 | C2 | semidirect |
| 5. C89×#3407 | C2 | semidirect |
| 53. C2×C16×C89 | D4 | semidirect |
| 139. #3407 | D89 | semidirect |
| 144. C89 | #13076 | semidirect |
| 184. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029914 | 2 |
| #26021981 | 2 |
| #26020302 | 2 |
| #26018351 | 2 |
| C89×#3407 | 2 |
| #13076 | 89 |