Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26020540 | C2 | semidirect |
| 4. #26018372 | C2 | semidirect |
| 19. #354×C89 | C4 | semidirect |
| 20. #353×C89 | C4 | semidirect |
| 143. C89 | #12969 | semidirect |
| 155. #354 | Dic89 | semidirect |
| 156. #353 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029323 | 2 |
| #26020636 | 2 |
| #26020540 | 2 |
| #26018372 | 2 |
| C89×#2126 | 2 |
| #12969 | 89 |