Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26018925 | C2 | semidirect |
| 4. #26018535 | C2 | semidirect |
| 5. C89×#1848 | C2 | semidirect |
| 118. #1848 | D89 | semidirect |
| 122. C89 | #9768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151971 | 2 |
| #26018925 | 2 |
| #26018921 | 2 |
| #26018535 | 2 |
| C89×#1848 | 2 |
| #9768 | 89 |