Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
736 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018958 | C2 | semidirect |
| 3. #26018829 | C2 | semidirect |
| 4. #26018800 | C2 | semidirect |
| 5. #26018800 | C2 | semidirect |
| 6. #26018720 | C2 | semidirect |
| 7. C89×#1535 | C2 | semidirect |
| 9. #19152321 | C4 | semidirect |
| 11. #19152270 | C4 | semidirect |
| 13. #19152253 | C4 | semidirect |
| 16. D4×D356 | C4 | semidirect |
| 24. #19151651 | C22 | semidirect |
| 25. #19151466 | C22 | semidirect |
| 35. #432×C89 | C22 | semidirect |
| 36. #432×C89 | C22 | semidirect |
| 287. #1535 | D89 | semidirect |
| 292. C89 | #8500 | semidirect |
| 310. #432 | C2×D89 | semidirect |
| 311. #432 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034626 | 2 |
| #26018958 | 2 |
| #26018829 | 2 |
| #26018800 | 2 |
| #26018720 | 2 |
| C89×#1535 | 2 |
| #8500 | 89 |