Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19151426 | C2 | semidirect |
| 3. #26018440 | C2 | direct (N × H) |
| 4. C2×M64×C89 | C2 | semidirect |
| 8. #19152030 | C4 | semidirect |
| 10. C2×Dic712 | C4 | semidirect |
| 12. C2×D1424 | C4 | semidirect |
| 15. #19151426 | C22 | semidirect |
| 18. M64×C89 | C22 | semidirect |
| 30. Dic712 | C2×C4 | semidirect |
| 34. D1424 | C2×C4 | semidirect |
| 111. C2×C89 | #1418 | semidirect |
| 115. C2×M64 | D89 | semidirect |
| 118. C89 | C2×#1418 | semidirect |
| 130. M64 | C2×D89 | semidirect |
| 225. C2 | #26018440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C2×#19151426 | 2 |
| #26018440 | 2 |
| C2×M64×C89 | 2 |
| C2×#1418 | 89 |