Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022535 | C2 | semidirect |
| 4. #26018303 | C2 | semidirect |
| 5. #26018222 | C2 | semidirect |
| 7. C89×#2225 | C2 | semidirect |
| 137. #2225 | D89 | semidirect |
| 142. C89 | #12401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032828 | 2 |
| #26022535 | 2 |
| #26019772 | 2 |
| #26018303 | 2 |
| #26018222 | 2 |
| #26018209 | 2 |
| C89×#2225 | 2 |
| #12401 | 89 |