Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
992 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26018370 | C2 | semidirect |
| 12. C24×C4×C89 | C4 | semidirect |
| 14. C22×C22⋊C4×C89 | C4 | semidirect |
| 17. #386×C89 | C4 | semidirect |
| 250. C89 | #12852 | semidirect |
| 252. C24×C4 | Dic89 | semidirect |
| 254. C22×C22⋊C4 | Dic89 | semidirect |
| 262. #386 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020173 | 2 |
| #26020167 | 2 |
| #26018370 | 2 |
| C2×#386×C89 | 2 |
| #12852 | 89 |