Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26020423 | C2 | semidirect |
| 3. #26018707 | C2 | semidirect |
| 6. C2×#19151320 | C2 | semidirect |
| 7. C89×#1493 | C2 | semidirect |
| 162. #1493 | D89 | semidirect |
| 166. C89 | #9858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030577 | 2 |
| #26020423 | 2 |
| #26018707 | 2 |
| #26018704 | 2 |
| #26018702 | 2 |
| C2×#19151320 | 2 |
| C89×#1493 | 2 |
| #9858 | 89 |