Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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. #29510221 | C2 | semidirect |
| 3. #29510150 | C2 | semidirect |
| 4. #29510142 | C2 | semidirect |
| 5. #29510141 | C2 | semidirect |
| 6. #29510125 | C2 | semidirect |
| 7. #131×C487 | C2 | semidirect |
| 9. #21441251 | C4 | semidirect |
| 10. #21441249 | C4 | semidirect |
| 11. #21441248 | C4 | semidirect |
| 12. #21441246 | C4 | semidirect |
| 51. C487 | #444 | semidirect |
| 55. #131 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510235 | 2 |
| #29510221 | 2 |
| #29510150 | 2 |
| #29510142 | 2 |
| #29510141 | 2 |
| #29510125 | 2 |
| #131×C487 | 2 |
| #444 | 487 |