Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018699 | C2 | semidirect |
| 4. #26018116 | C2 | semidirect |
| 169. C89 | #9493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028890 | 2 |
| #26018699 | 2 |
| #26018586 | 2 |
| #26018116 | 2 |
| C89×#2599 | 2 |
| #9493 | 89 |