Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018764 | C2 | semidirect |
| 4. #26018146 | C2 | semidirect |
| 17. #489×C89 | C4 | semidirect |
| 38. C4⋊Q8×C89 | C2×C4 | semidirect |
| 50. #97×C89 | C2×C4 | semidirect |
| 147. C89 | #9439 | semidirect |
| 150. #489 | Dic89 | semidirect |
| 168. C4⋊Q8 | C2×Dic89 | semidirect |
| 188. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023364 | 2 |
| #26018876 | 2 |
| #26018764 | 2 |
| #26018146 | 2 |
| C89×#3140 | 2 |
| #9439 | 89 |