Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021083 | C2 | semidirect |
| 3. #26018972 | C2 | semidirect |
| 4. #26018886 | C2 | semidirect |
| 5. #26018761 | C2 | semidirect |
| 6. #26018760 | C2 | semidirect |
| 7. C89×#1557 | C2 | semidirect |
| 11. #19152313 | C4 | semidirect |
| 13. D4×D356 | C4 | semidirect |
| 20. #19151655 | C22 | semidirect |
| 22. #19151444 | C22 | semidirect |
| 29. #432×C89 | C22 | semidirect |
| 30. #423×C89 | C22 | semidirect |
| 237. #1557 | D89 | semidirect |
| 241. C89 | #8491 | semidirect |
| 256. #432 | C2×D89 | semidirect |
| 257. #423 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26021083 | 2 |
| #26018972 | 2 |
| #26018886 | 2 |
| #26018761 | 2 |
| #26018760 | 2 |
| C89×#1557 | 2 |
| #8491 | 89 |