Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 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. #494×D89 | C2 | semidirect |
| 3. #486×D89 | C2 | semidirect |
| 4. #26019859 | C2 | semidirect |
| 5. #26019858 | C2 | semidirect |
| 6. #26019857 | C2 | semidirect |
| 7. #26019856 | C2 | semidirect |
| 8. C82×D89 | C2 | semidirect |
| 9. C89×#1709 | C2 | semidirect |
| 14. #19151978 | C22 | semidirect |
| 15. #19151977 | C22 | semidirect |
| 20. #19151946 | C22 | semidirect |
| 21. #19151945 | C22 | semidirect |
| 22. #19151944 | C22 | semidirect |
| 27. C8×#10623494 | C22 | semidirect |
| 28. C8×#10623494 | C22 | semidirect |
| 29. #494×C89 | C22 | semidirect |
| 31. #486×C89 | C22 | semidirect |
| 32. C82×C89 | C22 | semidirect |
| 146. D89 | #1709 | direct (N × H) |
| 154. #1709 | D89 | direct (N × H) |
| 156. C89 | C2×#1709 | semidirect |
| 164. #494 | C2×D89 | semidirect |
| 173. #486 | C2×D89 | semidirect |
| 179. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D89 | 2 |
| #493×D89 | 2 |
| #486×D89 | 2 |
| #26019859 | 2 |
| #26019858 | 2 |
| #26019857 | 2 |
| #26019856 | 2 |
| C82×D89 | 2 |
| C89×#1709 | 2 |
| C2×#1709 | 89 |