Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #26018130 | C2 | semidirect |
| 4. #26018119 | C2 | semidirect |
| 10. #19151466 | C4 | semidirect |
| 11. #19151461 | C4 | semidirect |
| 14. C4×C22⋊Dic89 | C4 | semidirect |
| 15. #19151444 | C4 | semidirect |
| 187. C89 | #8762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023192 | 2 |
| #26018570 | 2 |
| #26018130 | 2 |
| #26018119 | 2 |
| C89×#1799 | 2 |
| #8762 | 89 |