Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #29510208 | C2 | semidirect |
| 2. #29510208 | C2 | semidirect |
| 3. #29510201 | C2 | semidirect |
| 4. #29510199 | C2 | semidirect |
| 5. #29510198 | C2 | semidirect |
| 6. #29510197 | C2 | semidirect |
| 7. #29510194 | C2 | semidirect |
| 8. #29510192 | C2 | semidirect |
| 10. C4×C22⋊D487 | C2 | semidirect |
| 11. (C22⋊D487)⋊C4 | C2 | semidirect |
| 12. #29510174 | C2 | semidirect |
| 13. #29510171 | C2 | semidirect |
| 14. C2×C22⋊Dic487 | C2 | semidirect |
| 15. C2×C22⋊C4×C487 | C2 | semidirect |
| 16. C2×Dic974 | C22 | semidirect |
| 22. C2×C4×D487 | C22 | semidirect |
| 23. C4⋊Dic487 | C22 | semidirect |
| 24. C4⋊Dic487 | C22 | semidirect |
| 25. C4⋊Dic487 | C22 | semidirect |
| 26. Dic487⋊C4 | C22 | semidirect |
| 27. Dic487⋊C4 | C22 | semidirect |
| 28. Dic487⋊C4 | C22 | semidirect |
| 29. Dic487⋊C4 | C22 | semidirect |
| 30. Dic487⋊C4 | C22 | semidirect |
| 38. (C2×D487)⋊C4 | C22 | semidirect |
| 39. (C2×D487)⋊C4 | C22 | semidirect |
| 40. (C2×D487)⋊C4 | C22 | semidirect |
| 41. C4×Dic487 | C22 | semidirect |
| 42. C4×Dic487 | C22 | semidirect |
| 43. C4×Dic487 | C22 | semidirect |
| 110. C487 | #551 | semidirect |
| 126. C2×C22⋊C4 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510208 | 2 |
| #29510201 | 2 |
| #29510199 | 2 |
| #29510198 | 2 |
| #29510197 | 2 |
| #29510194 | 2 |
| #29510192 | 2 |
| #29510184 | 2 |
| C4×C22⋊D487 | 2 |
| (C22⋊D487)⋊C4 | 2 |
| #29510174 | 2 |
| #29510171 | 2 |
| C2×C22⋊Dic487 | 2 |
| C2×C22⋊C4×C487 | 2 |
| #551 | 487 |