Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26020349 | C2 | semidirect |
| 4. #26020327 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 10. #19151914 | C4 | semidirect |
| 11. #19151909 | C4 | semidirect |
| 38. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 39. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 56. C22⋊#10623494 | C2×C4 | semidirect |
| 239. C89 | #9525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030188 | 2 |
| #26023019 | 2 |
| #26020349 | 2 |
| #26020327 | 2 |
| #26018161 | 2 |
| #26018104 | 2 |
| C89×#1510 | 2 |
| #9525 | 89 |