Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26018824 | C2 | semidirect |
| 4. #26018119 | C2 | semidirect |
| 15. #399×C89 | C4 | semidirect |
| 17. #393×C89 | C4 | semidirect |
| 34. C22×Q8×C89 | C2×C4 | semidirect |
| 42. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 52. #95×C89 | C2×C4 | semidirect |
| 198. C89 | #9199 | semidirect |
| 203. #399 | Dic89 | semidirect |
| 205. #393 | Dic89 | semidirect |
| 215. C22×Q8 | C2×Dic89 | semidirect |
| 227. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 245. #95 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022866 | 2 |
| #26018824 | 2 |
| C2×#19151322 | 2 |
| #26018119 | 2 |
| C89×#2626 | 2 |
| #9199 | 89 |