Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26026049 | C2 | semidirect |
| 5. #26018771 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 227. #1826 | D89 | semidirect |
| 230. C89 | #9933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031059 | 2 |
| #26030192 | 2 |
| #26026049 | 2 |
| #26021088 | 2 |
| #26018771 | 2 |
| #26018157 | 2 |
| C89×#1826 | 2 |
| #9933 | 89 |