Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#11758416 | C2 | semidirect |
| 3. Q16×Dic31 | C2 | semidirect |
| 4. Dic31⋊C16 | C2 | semidirect |
| 5. #14520851 | C2 | semidirect |
| 6. #14520850 | C2 | semidirect |
| 7. C2×C31×SD32 | C2 | semidirect |
| 27. Q16×C31 | D4 | semidirect |
| 72. Dic31 | SD32 | semidirect |
| 74. C2×SD32 | D31 | semidirect |
| 98. C31 | #2207 | semidirect |
| 105. Q16 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758416 | 2 |
| #14521424 | 2 |
| Q16×Dic31 | 2 |
| Dic31⋊C16 | 2 |
| #14520851 | 2 |
| #14520850 | 2 |
| C2×C31×SD32 | 2 |
| #2207 | 31 |