Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022026 | C2 | semidirect |
| 3. C2×#19151422 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C89×#1388 | C2 | semidirect |
| 9. #19152016 | C4 | semidirect |
| 143. #1388 | D89 | semidirect |
| 145. C89 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26022026 | 2 |
| C2×#19151422 | 2 |
| #26020308 | 2 |
| #26020307 | 2 |
| #26018358 | 2 |
| C89×#1388 | 2 |
| #12833 | 89 |