Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
2528 conjugacy classes of subgroups; only the 1197 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 1197 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. C24×Dic31 | C2 | semidirect |
| 2. C2×D4×Dic31 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic31 | C2 | semidirect |
| 4. C22×C22⋊Dic31 | C2 | semidirect |
| 5. C22×C4×Dic31 | C2 | semidirect |
| 8. C22×D4×C31 | C4 | semidirect |
| 15. C23×Dic31 | C22 | semidirect |
| 16. C2×C22⋊Dic31 | C22 | semidirect |
| 17. D4×Dic31 | C22 | direct (N × H) |
| 18. C2×C4⋊Dic31 | C22 | semidirect |
| 19. C2×C4×Dic31 | C22 | semidirect |
| 22. C24×C31 | C2×C4 | semidirect |
| 25. C2×D4×C31 | C2×C4 | semidirect |
| 27. C22×C4×C31 | C2×C4 | semidirect |
| 32. C22×Dic31 | D4 | direct (N × H) |
| 36. C22×Dic31 | C23 | semidirect |
| 37. C22⋊Dic31 | C23 | semidirect |
| 38. C4⋊Dic31 | C23 | semidirect |
| 39. C4×Dic31 | C23 | semidirect |
| 44. C23×C31 | C22×C4 | semidirect |
| 49. D4×C31 | C22×C4 | semidirect |
| 50. C2×C4×C31 | C22×C4 | semidirect |
| 55. C2×Dic31 | C2×D4 | direct (N × H) |
| 63. C22×C31 | C4×D4 | semidirect |
| 65. C22×C31 | C23×C4 | semidirect |
| 69. C4×C31 | C23×C4 | semidirect |
| 72. Dic31 | C22×D4 | direct (N × H) |
| 80. C2×C31 | C2×C4×D4 | semidirect |
| 85. C22×D4 | Dic31 | direct (N × H) |
| 97. C31 | C22×C4×D4 | semidirect |
| 100. C24 | C2×Dic31 | semidirect |
| 103. C2×D4 | C2×Dic31 | direct (N × H) |
| 113. C22×C4 | C2×Dic31 | semidirect |
| 124. C23 | C22×Dic31 | semidirect |
| 127. D4 | C22×Dic31 | direct (N × H) |
| 135. C2×C4 | C22×Dic31 | semidirect |
| 140. C22 | D4×Dic31 | direct (N × H) |
| 144. C22 | C23×Dic31 | semidirect |
| 149. C4 | C23×Dic31 | semidirect |
| 151. C2 | C2×D4×Dic31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic31 | 2 |
| C2×D4×Dic31 | 2 |
| C22×C4⋊Dic31 | 2 |
| C22×C22⋊Dic31 | 2 |
| C22×C4×Dic31 | 2 |
| C23×D4×C31 | 2 |
| C22×C4×D4 | 31 |