Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 5. C2×#15668012 | C4 | semidirect |
| 12. #19151467 | C4 | semidirect |
| 13. C4×C4⋊Dic89 | C4 | semidirect |
| 36. #15667927 | Q8 | semidirect |
| 180. C89 | #13298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025205 | 2 |
| C4×#15667927 | 2 |
| #26018376 | 2 |
| C89×#1799 | 2 |
| #13298 | 89 |