Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #26020472 | C2 | semidirect |
| 5. #26018380 | C2 | semidirect |
| 6. #26018375 | C2 | semidirect |
| 7. C89×#1868 | C2 | semidirect |
| 193. #1868 | D89 | semidirect |
| 197. C89 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029310 | 2 |
| #26021891 | 2 |
| #26020670 | 2 |
| #26020472 | 2 |
| #26018380 | 2 |
| #26018375 | 2 |
| C89×#1868 | 2 |
| #12963 | 89 |