Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 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. #14521524 | C2 | direct (N × H) |
| 2. C2×D4×Dic31 | C2 | semidirect |
| 3. C2×#11758503 | C2 | semidirect |
| 4. C22×C22⋊Dic31 | C2 | semidirect |
| 7. C22×D4×C31 | C4 | semidirect |
| 11. C23×Dic31 | C22 | semidirect |
| 13. C2×C22⋊Dic31 | C22 | semidirect |
| 14. C2×C22⋊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. C24×C31 | C2×C4 | semidirect |
| 24. C2×D4×C31 | C2×C4 | semidirect |
| 25. C2×D4×C31 | C2×C4 | semidirect |
| 27. C22×C4×C31 | C2×C4 | semidirect |
| 32. C22×Dic31 | C23 | semidirect |
| 34. C22⋊Dic31 | C23 | semidirect |
| 35. C4⋊Dic31 | C23 | semidirect |
| 36. C4×Dic31 | C23 | semidirect |
| 43. C23×C31 | C22×C4 | semidirect |
| 47. D4×C31 | C22×C4 | semidirect |
| 49. C2×C4×C31 | C22×C4 | semidirect |
| 74. C2×C31 | #518 | semidirect |
| 78. C22×D4 | Dic31 | semidirect |
| 90. C31 | C2×#518 | semidirect |
| 92. C24 | C2×Dic31 | semidirect |
| 96. C2×D4 | C2×Dic31 | semidirect |
| 97. C2×D4 | C2×Dic31 | semidirect |
| 102. C22×C4 | C2×Dic31 | semidirect |
| 115. C23 | C22×Dic31 | semidirect |
| 119. D4 | C22×Dic31 | semidirect |
| 124. C2×C4 | C22×Dic31 | semidirect |
| 140. C2 | #14521524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521524 | 2 |
| C2×D4×Dic31 | 2 |
| C2×#11758503 | 2 |
| C22×C22⋊Dic31 | 2 |
| C23×D4×C31 | 2 |
| C2×#518 | 31 |