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. #26022538 | C2 | semidirect |
| 4. #26019771 | C2 | semidirect |
| 5. #26018305 | C2 | semidirect |
| 6. #26018235 | C2 | semidirect |
| 85. D8×C89 | Q16 | semidirect |
| 143. C89 | #12414 | semidirect |
| 205. D8 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033208 | 2 |
| #26022538 | 2 |
| #26022399 | 2 |
| #26019771 | 2 |
| #26018305 | 2 |
| #26018235 | 2 |
| C89×#1333 | 2 |
| #12414 | 89 |