Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018377 | C2 | semidirect |
| 8. C2×#117×C89 | C4 | semidirect |
| 9. C2×#117×C89 | C4 | semidirect |
| 11. #390×C89 | C4 | semidirect |
| 140. C89 | #12858 | semidirect |
| 142. C2×#117 | Dic89 | semidirect |
| 143. C2×#117 | Dic89 | semidirect |
| 147. #390 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020167 | 2 |
| #26018377 | 2 |
| C89×#2309 | 2 |
| #12858 | 89 |