Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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. #14521532 | C2 | semidirect |
| 2. #14521524 | C2 | semidirect |
| 3. #41×Dic31 | C2 | semidirect |
| 4. C2×D4×Dic31 | C2 | semidirect |
| 6. C31×H(5,𝔽2) | C4 | semidirect |
| 9. C23×Dic31 | C22 | semidirect |
| 10. C2×C22⋊Dic31 | C22 | semidirect |
| 11. Q8×Dic31 | C22 | semidirect |
| 12. Q8×Dic31 | C22 | semidirect |
| 13. D4×Dic31 | C22 | semidirect |
| 14. D4×Dic31 | C22 | semidirect |
| 15. D4×Dic31 | C22 | semidirect |
| 16. #11758503 | C22 | semidirect |
| 17. C2×C4⋊Dic31 | C22 | semidirect |
| 18. C2×C4×Dic31 | C22 | semidirect |
| 20. #41×C31 | C2×C4 | semidirect |
| 22. C2×D4×C31 | C2×C4 | semidirect |
| 36. C23×C31 | C22×C4 | semidirect |
| 38. Q8×C31 | C22×C4 | semidirect |
| 39. D4×C31 | C22×C4 | semidirect |
| 40. C2×C4×C31 | C22×C4 | semidirect |
| 57. Dic31 | H(5,𝔽2) | direct (N × H) |
| 67. H(5,𝔽2) | Dic31 | direct (N × H) |
| 80. C31 | C4×H(5,𝔽2) | semidirect |
| 82. #41 | C2×Dic31 | semidirect |
| 84. C2×D4 | C2×Dic31 | semidirect |
| 98. C23 | C22×Dic31 | semidirect |
| 100. Q8 | C22×Dic31 | semidirect |
| 101. D4 | C22×Dic31 | semidirect |
| 108. C2×C4 | C22×Dic31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521532 | 2 |
| #14521524 | 2 |
| #41×Dic31 | 2 |
| C2×D4×Dic31 | 2 |
| C2×C31×H(5,𝔽2) | 2 |
| C4×H(5,𝔽2) | 31 |