Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
912 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 325 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. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 5. C4×C22⋊Dic31 | C2 | semidirect |
| 6. #14520896 | C2 | semidirect |
| 7. C4×C22⋊C4×C31 | C2 | semidirect |
| 13. C2×C42×C31 | C22 | semidirect |
| 15. C2×(C2×D31)⋊C4 | C4 | semidirect |
| 19. C2×C4×Dic31 | C22 | semidirect |
| 20. C2×C4×Dic31 | C22 | semidirect |
| 21. C22⋊C4×D31 | C4 | semidirect |
| 22. C31×#95 | C22 | semidirect |
| 23. C31⋊#95 | C22 | semidirect |
| 24. C31⋊#95 | C22 | semidirect |
| 32. C22×C4×C31 | C2×C4 | semidirect |
| 37. C22×Dic31 | C2×C4 | semidirect |
| 42. C2×C4×D31 | C2×C4 | semidirect |
| 43. C22⋊C4×C31 | C2×C4 | semidirect |
| 45. C22⋊Dic31 | C2×C4 | semidirect |
| 46. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 47. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 48. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 61. C22×D31 | C42 | semidirect |
| 106. C4×C22⋊C4 | D31 | semidirect |
| 126. C2×C42 | C2×D31 | semidirect |
| 129. #95 | C2×D31 | semidirect |
| 130. C31 | #2273 | semidirect |
| 145. C22×C4 | C4×D31 | semidirect |
| 153. C22⋊C4 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D31)⋊C4 | 2 |
| C2×C22⋊C4×D31 | 2 |
| C22⋊C4×Dic31 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| C4×C22⋊Dic31 | 2 |
| #14520896 | 2 |
| C4×C22⋊C4×C31 | 2 |
| #2273 | 31 |