Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
936 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031442 | C2 | semidirect |
| 3. #26019563 | C2 | semidirect |
| 4. #26019550 | C2 | semidirect |
| 5. #26018876 | C2 | semidirect |
| 6. #26018854 | C2 | semidirect |
| 7. C2×#563×C89 | C2 | semidirect |
| 11. #19152008 | C22 | semidirect |
| 15. #19151964 | C22 | semidirect |
| 21. #19151340 | C22 | semidirect |
| 187. C2×#563 | D89 | semidirect |
| 194. C89 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031442 | 2 |
| #26030716 | 2 |
| #26019563 | 2 |
| #26019550 | 2 |
| #26018876 | 2 |
| #26018854 | 2 |
| C2×#563×C89 | 2 |
| #18994 | 89 |