Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #14521523 | C2 | semidirect |
| 3. #14521055 | C2 | semidirect |
| 4. #14521053 | C2 | semidirect |
| 5. C2×#11758411 | C2 | semidirect |
| 6. #14520809 | C2 | semidirect |
| 7. C31×#339 | C2 | semidirect |
| 19. #11758451 | C4 | semidirect |
| 40. C2×D124 | C2×C4 | semidirect |
| 46. C4⋊C4×C31 | D4 | semidirect |
| 50. C42×C31 | C2×C4 | semidirect |
| 53. C4⋊Dic31 | D4 | semidirect |
| 115. #339 | D31 | semidirect |
| 138. C31 | #1887 | semidirect |
| 165. C4⋊C4 | D124 | semidirect |
| 172. C42 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758451 | 2 |
| #14521523 | 2 |
| #14521055 | 2 |
| #14521053 | 2 |
| C2×#11758411 | 2 |
| #14520809 | 2 |
| C31×#339 | 2 |
| #1887 | 31 |