Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19151406 | C2 | semidirect |
| 3. #26020290 | C2 | semidirect |
| 4. #26018348 | C2 | semidirect |
| 5. C22×M32×C89 | C2 | semidirect |
| 51. C2×C16×C89 | D4 | semidirect |
| 138. C22×M32 | D89 | semidirect |
| 143. C89 | #13064 | semidirect |
| 182. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029833 | 2 |
| C2×#19151406 | 2 |
| #26020290 | 2 |
| #26018348 | 2 |
| C22×M32×C89 | 2 |
| #13064 | 89 |