Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 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. #26022160 | C2 | semidirect |
| 3. #26019613 | C2 | semidirect |
| 4. #26018297 | C2 | semidirect |
| 5. C89×#1372 | C2 | semidirect |
| 51. C16×C89 | SD16 | semidirect |
| 87. #1372 | D89 | semidirect |
| 89. C89 | #12442 | semidirect |
| 135. C16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022502 | 2 |
| #26022160 | 2 |
| #26019613 | 2 |
| #26018297 | 2 |
| C89×#1372 | 2 |
| #12442 | 89 |