Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 1. C2×#19151432 | C2 | semidirect |
| 2. #26022036 | C2 | semidirect |
| 3. #26018439 | C2 | semidirect |
| 7. #19151432 | C22 | semidirect |
| 9. #19151426 | C22 | semidirect |
| 14. #508×C89 | C4 | semidirect |
| 16. C2×Q32×C89 | C4 | semidirect |
| 18. C2×D16×C89 | C4 | semidirect |
| 117. C89 | #13622 | semidirect |
| 121. #508 | Dic89 | semidirect |
| 123. C2×Q32 | Dic89 | semidirect |
| 125. C2×D16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151432 | 2 |
| #26022036 | 2 |
| #26018439 | 2 |
| C2×#508×C89 | 2 |
| #13622 | 89 |