Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 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. #26031255 | C2 | semidirect |
| 2. #26030638 | C2 | semidirect |
| 3. #26019558 | C2 | semidirect |
| 4. #26018876 | C2 | semidirect |
| 5. #26018850 | C2 | semidirect |
| 7. #19152155 | C22 | semidirect |
| 8. #19151993 | C22 | semidirect |
| 9. #19151957 | C22 | semidirect |
| 10. #19151957 | C22 | semidirect |
| 15. #19151655 | C22 | semidirect |
| 18. C4×#13083558 | C22 | semidirect |
| 19. #19151338 | C22 | semidirect |
| 20. #19151338 | C22 | semidirect |
| 33. #15668012 | C23 | semidirect |
| 44. #15667923 | C23 | semidirect |
| 45. #15667923 | C23 | semidirect |
| 189. C89 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031255 | 2 |
| #26030638 | 2 |
| #26019558 | 2 |
| #26018876 | 2 |
| #26018850 | 2 |
| C2×H(3,𝔽4)×C89 | 2 |
| #18997 | 89 |