Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×Dic124 | C2 | semidirect |
| 4. #14520877 | C2 | semidirect |
| 5. #14520854 | C2 | semidirect |
| 7. C4×C16×C31 | C2 | semidirect |
| 19. #11758388 | C4 | direct (N × H) |
| 32. Dic124 | C2×C4 | semidirect |
| 36. C16×C31 | C2×C4 | semidirect |
| 58. C4×C31 | SD32 | semidirect |
| 70. C4×C16 | D31 | semidirect |
| 87. C31 | C4×SD32 | semidirect |
| 104. C16 | C4×D31 | semidirect |
| 128. C4 | #11758388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758388 | 2 |
| C4×Dic124 | 2 |
| C4×D248 | 2 |
| #14520877 | 2 |
| #14520854 | 2 |
| #14520851 | 2 |
| C4×C16×C31 | 2 |
| C4×SD32 | 31 |