Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. Q8×Dic433 | C2 | semidirect |
| 4. #28357151 | C2 | semidirect |
| 6. C8×Dic433 | C2 | semidirect |
| 7. #103×C433 | C2 | semidirect |
| 10. #20294084 | C4 | semidirect |
| 27. #16812358 | C2×C4 | semidirect |
| 29. Q8×C433 | C2×C4 | semidirect |
| 44. Dic433 | SD16 | semidirect |
| 49. C433 | C4×SD16 | semidirect |
| 55. #103 | D433 | semidirect |
| 72. Q8 | C4×D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294084 | 2 |
| Q8×Dic433 | 2 |
| #28357182 | 2 |
| #28357151 | 2 |
| #28357142 | 2 |
| C8×Dic433 | 2 |
| #103×C433 | 2 |
| C4×SD16 | 433 |