Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
292 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. C22×#13083549 | C4 | semidirect |
| 14. C22⋊C16×C89 | C4 | semidirect |
| 116. C89 | #7200 | semidirect |
| 126. C22⋊C16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13083549 | 2 |
| #26020028 | 2 |
| C89×#2112 | 2 |
| #7200 | 89 |