Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. D8×Dic31 | C2 | semidirect |
| 3. #14521131 | C2 | semidirect |
| 4. #14520874 | C2 | semidirect |
| 5. #14520851 | C2 | semidirect |
| 6. C16×Dic31 | C2 | semidirect |
| 7. C31×#357 | C2 | semidirect |
| 15. #11758414 | C4 | semidirect |
| 25. D8×C31 | C2×C4 | semidirect |
| 34. D248 | C2×C4 | semidirect |
| 36. C31⋊C16 | C2×C4 | semidirect |
| 66. Dic31 | D16 | semidirect |
| 72. #357 | D31 | semidirect |
| 91. C31 | C4×D16 | semidirect |
| 99. D8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758414 | 2 |
| D8×Dic31 | 2 |
| #14521131 | 2 |
| #14520874 | 2 |
| #14520851 | 2 |
| C16×Dic31 | 2 |
| C31×#357 | 2 |
| C4×D16 | 31 |