Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. #29510180 | C2 | semidirect |
| 4. #29510138 | C2 | semidirect |
| 6. #29510125 | C2 | semidirect |
| 7. #107×C487 | C2 | semidirect |
| 11. #21441250 | C4 | semidirect |
| 22. Dic974 | C2×C4 | semidirect |
| 33. C8×C487 | C2×C4 | semidirect |
| 49. C487 | #440 | semidirect |
| 54. #107 | D487 | semidirect |
| 83. C8 | C4×D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21441250 | 2 |
| #29510180 | 2 |
| #29510177 | 2 |
| #29510138 | 2 |
| #29510135 | 2 |
| #29510125 | 2 |
| #107×C487 | 2 |
| #440 | 487 |