Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #26020351 | C2 | semidirect |
| 4. #26018785 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 7. C89×#3095 | C2 | semidirect |
| 230. #3095 | D89 | semidirect |
| 237. C89 | #9944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025411 | 2 |
| #26024522 | 2 |
| #26020351 | 2 |
| #26018785 | 2 |
| #26018578 | 2 |
| #26018106 | 2 |
| C89×#3095 | 2 |
| #9944 | 89 |