Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26030971 | C2 | semidirect |
| 3. #26030648 | C2 | semidirect |
| 4. #26019906 | C2 | semidirect |
| 5. #26019900 | C2 | semidirect |
| 6. #26019894 | C2 | semidirect |
| 7. #26019865 | C2 | semidirect |
| 8. #26018555 | C2 | semidirect |
| 9. C89×#3139 | C2 | semidirect |
| 162. #3139 | D89 | semidirect |
| 168. C89 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030990 | 2 |
| #26030971 | 2 |
| #26030648 | 2 |
| #26019906 | 2 |
| #26019900 | 2 |
| #26019894 | 2 |
| #26019865 | 2 |
| #26018555 | 2 |
| C89×#3139 | 2 |
| #19754 | 89 |