Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19151393 | C2 | semidirect |
| 4. #26018377 | C2 | semidirect |
| 15. C2×C4⋊Q8×C89 | C4 | semidirect |
| 17. C2×C22⋊Q8×C89 | C4 | semidirect |
| 20. #391×C89 | C4 | semidirect |
| 24. C4×C22⋊C4×C89 | C4 | semidirect |
| 250. C89 | #13091 | semidirect |
| 252. C2×C4⋊Q8 | Dic89 | semidirect |
| 254. C2×C22⋊Q8 | Dic89 | semidirect |
| 263. #391 | Dic89 | semidirect |
| 268. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151572 | 2 |
| C2×#19151393 | 2 |
| #26020170 | 2 |
| #26018377 | 2 |
| C89×#2432 | 2 |
| #13091 | 89 |