Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26018427 | C2 | semidirect |
| 12. C2×#125×C89 | C4 | semidirect |
| 15. #488×C89 | C4 | semidirect |
| 19. C4×M16×C89 | C4 | semidirect |
| 136. C89 | #13604 | semidirect |
| 138. C2×#125 | Dic89 | semidirect |
| 141. #488 | Dic89 | semidirect |
| 147. C4×M16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021937 | 2 |
| #26021917 | 2 |
| #26018427 | 2 |
| C89×#3142 | 2 |
| #13604 | 89 |