Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
364 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022051 | C2 | semidirect |
| 3. #26018177 | C2 | semidirect |
| 4. C89×#2162 | C2 | semidirect |
| 124. #2162 | D89 | semidirect |
| 126. C89 | #11490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028965 | 2 |
| #26022051 | 2 |
| #26018177 | 2 |
| C89×#2162 | 2 |
| #11490 | 89 |