Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C22×Dic866 | C2 | semidirect |
| 2. #28357250 | C2 | direct (N × H) |
| 3. C2×#20294087 | C2 | semidirect |
| 4. C2×#20294085 | C2 | semidirect |
| 5. C2×#20294081 | C2 | semidirect |
| 10. C2×Dic866 | C22 | semidirect |
| 12. #20294087 | C22 | semidirect |
| 13. #20294085 | C22 | semidirect |
| 14. #20294081 | C22 | semidirect |
| 54. C2×C433 | #137 | semidirect |
| 56. C433 | C2×#137 | semidirect |
| 111. C2 | #28357250 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic866 | 2 |
| #28357250 | 2 |
| C2×#20294087 | 2 |
| C2×#20294085 | 2 |
| C2×#20294081 | 2 |
| C2×#41×C433 | 2 |
| C2×#137 | 433 |