Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C22×#15667953 | C2 | semidirect |
| 2. C2×#19151868 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. #26021866 | C2 | semidirect |
| 6. #26018345 | C2 | semidirect |
| 7. C2×#472×C89 | C2 | semidirect |
| 200. C2×#472 | D89 | semidirect |
| 205. C89 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667953 | 2 |
| C2×#19151868 | 2 |
| C2×#19151411 | 2 |
| C2×#19151410 | 2 |
| #26021866 | 2 |
| #26018345 | 2 |
| C2×#472×C89 | 2 |
| #13313 | 89 |