Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018412 | C2 | direct (N × H) |
| 13. C2×C4⋊Q8×C89 | C4 | semidirect |
| 17. #497×C89 | C4 | semidirect |
| 19. C2×#97×C89 | C4 | semidirect |
| 40. C4⋊Q8×C89 | C2×C4 | semidirect |
| 50. #97×C89 | C2×C4 | semidirect |
| 151. C2×C89 | #1407 | semidirect |
| 157. C89 | C2×#1407 | semidirect |
| 160. C2×C4⋊Q8 | Dic89 | semidirect |
| 164. #497 | Dic89 | semidirect |
| 168. C2×#97 | Dic89 | semidirect |
| 188. C4⋊Q8 | C2×Dic89 | semidirect |
| 203. #97 | C2×Dic89 | semidirect |
| 303. C2 | #26018412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151395 | 2 |
| C2×#19151393 | 2 |
| #26018412 | 2 |
| C2×#497×C89 | 2 |
| C2×#1407 | 89 |