Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018272 | C2 | semidirect |
| 5. C2×#15668012 | C4 | semidirect |
| 7. #19151510 | C4 | semidirect |
| 13. C4×C4⋊Dic89 | C4 | semidirect |
| 167. C89 | #11900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025425 | 2 |
| #26018570 | 2 |
| #26018272 | 2 |
| C89×#1799 | 2 |
| #11900 | 89 |