Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26020288 | C2 | semidirect |
| 4. #26018129 | C2 | semidirect |
| 5. C89×#1293 | C2 | semidirect |
| 104. C22×D89 | #108 | semidirect |
| 121. C2×Dic89 | #108 | semidirect |
| 166. #1293 | D89 | semidirect |
| 167. C89 | #8612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151661 | 2 |
| #26020288 | 2 |
| #26018588 | 2 |
| #26018129 | 2 |
| C89×#1293 | 2 |
| #8612 | 89 |