Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #26033355 | C2 | semidirect |
| 3. #26021987 | C2 | semidirect |
| 4. C2×#19151407 | C2 | semidirect |
| 5. C89×#2912 | C2 | semidirect |
| 7. #19152415 | C4 | semidirect |
| 9. #19152403 | C4 | semidirect |
| 13. C2×#15667952 | C22 | semidirect |
| 14. #19151407 | C22 | semidirect |
| 15. #19151407 | C22 | semidirect |
| 19. #427×C89 | C22 | semidirect |
| 20. C2×#106×C89 | C22 | semidirect |
| 31. #15668034 | C2×C4 | semidirect |
| 33. C2×Dic356 | C2×C4 | semidirect |
| 35. C2×D712 | C2×C4 | semidirect |
| 128. #2912 | D89 | semidirect |
| 131. C89 | #33388 | semidirect |
| 143. #427 | C2×D89 | semidirect |
| 144. C2×#106 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| #26033355 | 2 |
| #26021987 | 2 |
| C2×#19151407 | 2 |
| C89×#2912 | 2 |
| #33388 | 89 |