Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #29510262 | C2 | semidirect |
| 2. #29510261 | C2 | semidirect |
| 3. #29510248 | C2 | semidirect |
| 4. #29510243 | C2 | semidirect |
| 5. #29510237 | C2 | semidirect |
| 6. C2×#21441250 | C2 | semidirect |
| 7. #131×C487 | C2 | semidirect |
| 10. #21441261 | C22 | semidirect |
| 12. C2×Dic974 | C22 | semidirect |
| 16. Dic1948 | C22 | semidirect |
| 17. #21441250 | C22 | semidirect |
| 18. #21441250 | C22 | semidirect |
| 19. #21441250 | C22 | semidirect |
| 20. D3896 | C22 | semidirect |
| 22. M16×C487 | C22 | semidirect |
| 23. C2×C8×C487 | C22 | semidirect |
| 53. C487 | #577 | semidirect |
| 61. #131 | D487 | semidirect |
| 76. M16 | C2×D487 | semidirect |
| 77. C2×C8 | C2×D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510262 | 2 |
| #29510261 | 2 |
| #29510248 | 2 |
| #29510243 | 2 |
| #29510237 | 2 |
| C2×#21441250 | 2 |
| #131×C487 | 2 |
| #577 | 487 |