Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 125 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. #101×Dic89 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 16. #19151395 | C4 | semidirect |
| 20. #355×C89 | C4 | semidirect |
| 35. #15667931 | C2×C4 | semidirect |
| 50. #101×C89 | C2×C4 | semidirect |
| 159. C89 | #12632 | semidirect |
| 173. #355 | Dic89 | semidirect |
| 199. #101 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022965 | 2 |
| C2×#19151395 | 2 |
| #101×Dic89 | 2 |
| #26018378 | 2 |
| C2×#355×C89 | 2 |
| #12632 | 89 |