Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26019161 | C2 | semidirect |
| 3. #26018318 | C2 | semidirect |
| 4. #26018222 | C2 | semidirect |
| 6. #26018172 | C2 | semidirect |
| 66. C16×C89 | M16 | semidirect |
| 110. C89 | #12087 | semidirect |
| 169. C16 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019166 | 2 |
| #26019161 | 2 |
| #26018318 | 2 |
| #26018222 | 2 |
| #26018219 | 2 |
| #26018172 | 2 |
| C89×#2175 | 2 |
| #12087 | 89 |