Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. #26022460 | C2 | semidirect |
| 3. #26022443 | C2 | semidirect |
| 4. #26022038 | C2 | semidirect |
| 5. #26021962 | C2 | semidirect |
| 6. #26021863 | C2 | semidirect |
| 7. C2×#427×C89 | C2 | semidirect |
| 16. #19151425 | C22 | semidirect |
| 17. #19151423 | C22 | semidirect |
| 18. #19151401 | C22 | semidirect |
| 19. #19151398 | C22 | semidirect |
| 145. C2×#427 | D89 | semidirect |
| 151. C89 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029833 | 2 |
| #26022460 | 2 |
| #26022443 | 2 |
| #26022038 | 2 |
| #26021962 | 2 |
| #26021863 | 2 |
| C2×#427×C89 | 2 |
| #33647 | 89 |