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 |
|---|---|---|
| 2. #28357251 | C2 | direct (N × H) |
| 3. C2×#20294087 | C2 | semidirect |
| 4. C2×#20294084 | C2 | semidirect |
| 5. C2×#20294081 | C2 | semidirect |
| 6. C22×Q8×C433 | C2 | semidirect |
| 13. #20294087 | C22 | semidirect |
| 14. #20294084 | C22 | semidirect |
| 15. #20294081 | C22 | semidirect |
| 20. C2×Q8×C433 | C22 | semidirect |
| 53. C2×C433 | #137 | semidirect |
| 56. C433 | C2×#137 | semidirect |
| 59. C22×Q8 | D433 | semidirect |
| 70. C2×Q8 | C2×D433 | semidirect |
| 111. C2 | #28357251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294097 | 2 |
| #28357251 | 2 |
| C2×#20294087 | 2 |
| C2×#20294084 | 2 |
| C2×#20294081 | 2 |
| C22×Q8×C433 | 2 |
| C2×#137 | 433 |