Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 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 | semidirect |
| 14. C2×C4⋊Q8×C89 | C4 | semidirect |
| 15. #497×C89 | C4 | semidirect |
| 19. C4×M16×C89 | C4 | semidirect |
| 153. C89 | #13580 | semidirect |
| 157. C2×C4⋊Q8 | Dic89 | semidirect |
| 158. #497 | Dic89 | semidirect |
| 164. C4×M16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021937 | 2 |
| #26021917 | 2 |
| #26018412 | 2 |
| C89×#3152 | 2 |
| #13580 | 89 |