Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 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. #29510261 | C2 | semidirect |
| 2. #29510241 | C2 | semidirect |
| 3. #29510240 | C2 | semidirect |
| 4. #29510235 | C2 | semidirect |
| 5. C2×#21441246 | C2 | semidirect |
| 6. #29510222 | C2 | semidirect |
| 7. H(5,𝔽2)×C487 | C2 | semidirect |
| 9. #21441261 | C22 | semidirect |
| 10. C2×D1948 | C22 | semidirect |
| 12. #21441251 | C22 | semidirect |
| 13. #21441249 | C22 | semidirect |
| 14. #21441248 | C22 | semidirect |
| 15. #21441246 | C22 | semidirect |
| 16. #21441246 | C22 | semidirect |
| 17. #21441245 | C22 | semidirect |
| 18. C2×C487⋊C8 | C22 | semidirect |
| 21. #41×C487 | C22 | semidirect |
| 23. C2×D4×C487 | C22 | semidirect |
| 54. C487 | #576 | semidirect |
| 57. H(5,𝔽2) | D487 | semidirect |
| 67. #41 | C2×D487 | semidirect |
| 71. C2×D4 | C2×D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510261 | 2 |
| #29510241 | 2 |
| #29510240 | 2 |
| #29510235 | 2 |
| C2×#21441246 | 2 |
| #29510222 | 2 |
| H(5,𝔽2)×C487 | 2 |
| #576 | 487 |