Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021064 | C2 | semidirect |
| 2. #26018876 | C2 | semidirect |
| 3. #26018790 | C2 | semidirect |
| 4. #26018712 | C2 | semidirect |
| 6. #19151655 | C22 | semidirect |
| 9. C2×C4×#10623494 | C22 | semidirect |
| 10. #19151464 | C22 | semidirect |
| 17. #563×C89 | C4 | semidirect |
| 18. #562×C89 | C4 | semidirect |
| 19. H(3,𝔽4)×C89 | C4 | semidirect |
| 243. C89 | #8528 | semidirect |
| 244. #563 | Dic89 | semidirect |
| 245. #562 | Dic89 | semidirect |
| 246. H(3,𝔽4) | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021064 | 2 |
| #26018876 | 2 |
| #26018790 | 2 |
| #26018712 | 2 |
| C89×#3545 | 2 |
| #8528 | 89 |