Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14521067 | C2 | semidirect |
| 4. #14521065 | C2 | semidirect |
| 5. C2×#11758411 | C2 | semidirect |
| 6. #14520805 | C2 | semidirect |
| 7. C31×H(3,ℤ/4) | C2 | semidirect |
| 19. #11758452 | C4 | semidirect |
| 20. #11758451 | C4 | semidirect |
| 38. C2×D124 | C2×C4 | semidirect |
| 42. C2×Dic62 | C2×C4 | semidirect |
| 50. C42×C31 | C2×C4 | semidirect |
| 51. C42×C31 | D4 | semidirect |
| 56. C4×Dic31 | D4 | semidirect |
| 117. H(3,ℤ/4) | D31 | semidirect |
| 141. C31 | #1911 | semidirect |
| 175. C42 | C4×D31 | semidirect |
| 176. C42 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521618 | 2 |
| #14521523 | 2 |
| #14521067 | 2 |
| #14521065 | 2 |
| C2×#11758411 | 2 |
| #14520805 | 2 |
| C31×H(3,ℤ/4) | 2 |
| #1911 | 31 |