Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 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. #26022036 | C2 | semidirect |
| 3. #26018440 | C2 | semidirect |
| 4. C2×M64×C89 | C2 | semidirect |
| 8. #19152030 | C4 | semidirect |
| 10. C2×Dic712 | C4 | semidirect |
| 12. C2×D1424 | C4 | semidirect |
| 14. #19151426 | C22 | semidirect |
| 18. M64×C89 | C22 | semidirect |
| 114. C2×M64 | D89 | semidirect |
| 117. C89 | #13622 | semidirect |
| 129. M64 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| #26022036 | 2 |
| #26018440 | 2 |
| C2×M64×C89 | 2 |
| #13622 | 89 |