Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 9. #19151353 | C4 | semidirect |
| 12. C2×#97×C89 | C4 | semidirect |
| 143. C89 | #7036 | semidirect |
| 148. C2×#97 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020014 | 2 |
| #26018479 | 2 |
| C89×#1749 | 2 |
| #7036 | 89 |