Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022535 | C2 | semidirect |
| 3. #26019767 | C2 | semidirect |
| 4. #26018303 | C2 | semidirect |
| 5. #26018233 | C2 | semidirect |
| 84. D8×C89 | Q16 | semidirect |
| 143. C89 | #12414 | semidirect |
| 205. D8 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033208 | 2 |
| #26022535 | 2 |
| #26019767 | 2 |
| #26018303 | 2 |
| #26018233 | 2 |
| #26018219 | 2 |
| C89×#2226 | 2 |
| #12414 | 89 |