Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
850 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 850 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 |
|---|---|---|
| 1. #26031458 | C2 | semidirect |
| 3. #26019586 | C2 | semidirect |
| 5. #26018854 | C2 | semidirect |
| 8. #19152008 | C22 | semidirect |
| 9. #19151968 | C22 | semidirect |
| 19. #19151340 | C22 | semidirect |
| 169. C89 | #18999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031458 | 2 |
| #26030638 | 2 |
| #26019586 | 2 |
| #26018876 | 2 |
| #26018854 | 2 |
| C2×#563×C89 | 2 |
| #18999 | 89 |