Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×Q16×D31 | C2 | semidirect |
| 2. C2×SD16×D31 | C2 | semidirect |
| 4. #124×D31 | C2 | semidirect |
| 5. #14521434 | C2 | semidirect |
| 6. #14521433 | C2 | semidirect |
| 7. #14521432 | C2 | semidirect |
| 8. #14521431 | C2 | semidirect |
| 9. #14521430 | C2 | semidirect |
| 10. C4×C8×D31 | C2 | semidirect |
| 11. C31×#495 | C2 | semidirect |
| 14. C2×Q16×C31 | C22 | semidirect |
| 15. C2×SD16×C31 | C22 | semidirect |
| 17. C31×#124 | C22 | semidirect |
| 18. #11758524 | C22 | semidirect |
| 19. C2×#92482 | C22 | semidirect |
| 20. C2×#92481 | C22 | semidirect |
| 21. #11758513 | C22 | semidirect |
| 22. C2×#92480 | C22 | semidirect |
| 27. C2×Dic124 | C22 | semidirect |
| 29. C2×#92470 | C22 | semidirect |
| 34. #11758452 | C22 | semidirect |
| 36. C4×C8×C31 | C22 | semidirect |
| 37. C8×Dic31 | C22 | semidirect |
| 38. C8×Dic31 | C22 | semidirect |
| 39. C4×C31⋊C8 | C22 | semidirect |
| 131. #495 | D31 | direct (N × H) |
| 137. D31 | #495 | direct (N × H) |
| 143. C2×Q16 | C2×D31 | semidirect |
| 148. C2×SD16 | C2×D31 | semidirect |
| 159. #124 | C2×D31 | semidirect |
| 165. C4×C8 | C2×D31 | semidirect |
| 166. C31 | C2×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D31 | 2 |
| C2×SD16×D31 | 2 |
| C2×D8×D31 | 2 |
| #124×D31 | 2 |
| #14521434 | 2 |
| #14521433 | 2 |
| #14521432 | 2 |
| #14521431 | 2 |
| #14521430 | 2 |
| C4×C8×D31 | 2 |
| C31×#495 | 2 |
| C2×#495 | 31 |