Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#19152334 | C2 | semidirect |
| 3. #26030375 | C2 | semidirect |
| 4. #26019374 | C2 | semidirect |
| 5. #26019312 | C2 | semidirect |
| 6. #26018698 | C2 | semidirect |
| 7. C89×#1555 | C2 | semidirect |
| 21. #19151894 | C22 | semidirect |
| 22. #19151799 | C22 | semidirect |
| 26. #19151328 | C22 | semidirect |
| 170. #1555 | D89 | semidirect |
| 172. C89 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152334 | 2 |
| #26030702 | 2 |
| #26030375 | 2 |
| #26019374 | 2 |
| #26019312 | 2 |
| #26018698 | 2 |
| C89×#1555 | 2 |
| #18526 | 89 |