Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 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. Q16×Dic31 | C2 | semidirect |
| 3. #14520877 | C2 | semidirect |
| 4. #14520853 | C2 | semidirect |
| 6. C16×Dic31 | C2 | semidirect |
| 12. C31×SD32 | C4 | semidirect |
| 24. Q16×C31 | C2×C4 | semidirect |
| 35. C16×C31 | C2×C4 | semidirect |
| 63. Dic31 | SD32 | direct (N × H) |
| 79. SD32 | Dic31 | direct (N × H) |
| 87. C31 | C4×SD32 | semidirect |
| 92. Q16 | C2×Dic31 | semidirect |
| 104. C16 | C2×Dic31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic31 | 2 |
| D8×Dic31 | 2 |
| #14520877 | 2 |
| #14520853 | 2 |
| #14520850 | 2 |
| C16×Dic31 | 2 |
| C2×C31×SD32 | 2 |
| C4×SD32 | 31 |