Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #26020188 | C2 | semidirect |
| 5. #26020186 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 19. #19151519 | C4 | semidirect |
| 20. #19151511 | C4 | semidirect |
| 249. #1289 | D89 | semidirect |
| 250. C89 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029278 | 2 |
| #26023618 | 2 |
| #26020237 | 2 |
| #26020188 | 2 |
| #26020186 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9471 | 89 |