Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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 |
|---|---|---|
| 3. C22×C4⋊Dic31 | C2 | semidirect |
| 4. C22×Dic31⋊C4 | C2 | semidirect |
| 5. C2×C4⋊C4×D31 | C2 | direct (N × H) |
| 6. C22×C4⋊C4×C31 | C2 | semidirect |
| 13. C22×C4×D31 | C4 | semidirect |
| 16. C2×C4⋊C4×C31 | C22 | semidirect |
| 17. C2×C4⋊Dic31 | C22 | semidirect |
| 18. C2×Dic31⋊C4 | C22 | semidirect |
| 19. C4⋊C4×D31 | C22 | direct (N × H) |
| 26. C22×C4×C31 | C2×C4 | semidirect |
| 30. C22×Dic31 | C2×C4 | semidirect |
| 34. C2×C4×D31 | C2×C4 | semidirect |
| 37. C4⋊C4×C31 | C23 | semidirect |
| 38. C4⋊Dic31 | C23 | semidirect |
| 39. Dic31⋊C4 | C23 | semidirect |
| 44. C22×D31 | C4⋊C4 | direct (N × H) |
| 50. C2×C4×C31 | C22×C4 | semidirect |
| 54. C2×Dic31 | C22×C4 | semidirect |
| 58. C4×D31 | C22×C4 | semidirect |
| 60. C22×C31 | C2×C4⋊C4 | semidirect |
| 65. C2×D31 | C2×C4⋊C4 | direct (N × H) |
| 70. C4×C31 | C23×C4 | semidirect |
| 72. Dic31 | C23×C4 | semidirect |
| 78. C22×C4⋊C4 | D31 | direct (N × H) |
| 79. C2×C31 | C22×C4⋊C4 | semidirect |
| 83. D31 | C22×C4⋊C4 | direct (N × H) |
| 96. C2×C4⋊C4 | C2×D31 | direct (N × H) |
| 97. C31 | C23×C4⋊C4 | semidirect |
| 112. C22×C4 | C4×D31 | semidirect |
| 117. C4⋊C4 | C22×D31 | direct (N × H) |
| 134. C2×C4 | C2×C4×D31 | semidirect |
| 141. C22 | C4⋊C4×D31 | direct (N × H) |
| 149. C4 | C22×C4×D31 | semidirect |
| 151. C2 | C2×C4⋊C4×D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D31 | 2 |
| C22×C4⋊Dic31 | 2 |
| C22×Dic31⋊C4 | 2 |
| C2×C4⋊C4×D31 | 2 |
| C22×C4⋊C4×C31 | 2 |
| C23×C4⋊C4 | 31 |