Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1450 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26029502 | C2 | semidirect |
| 2. #26023587 | C2 | semidirect |
| 3. #26019221 | C2 | semidirect |
| 4. #26019187 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 7. C2×#537×C89 | C2 | semidirect |
| 12. #19151736 | C22 | semidirect |
| 13. #19151731 | C22 | semidirect |
| 16. #19151518 | C22 | semidirect |
| 17. #19151515 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151324 | C22 | semidirect |
| 190. C2×C4×C89 | AGL(1,ℤ/8) | semidirect |
| 242. C2×#537 | D89 | semidirect |
| 249. C89 | #18142 | semidirect |
| 445. C2×C4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029502 | 2 |
| #26023587 | 2 |
| #26019221 | 2 |
| #26019187 | 2 |
| #26018781 | 2 |
| #26018582 | 2 |
| C2×#537×C89 | 2 |
| #18142 | 89 |