Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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. #14521454 | C2 | semidirect |
| 3. #14521453 | C2 | semidirect |
| 4. #14521452 | C2 | semidirect |
| 7. C31×#500 | C2 | semidirect |
| 44. C8×D31 | Q8 | semidirect |
| 61. C8×C31 | C2×Q8 | semidirect |
| 62. C31⋊C8 | C2×Q8 | semidirect |
| 80. #500 | D31 | direct (N × H) |
| 86. D31 | #500 | direct (N × H) |
| 103. C31 | C2×#500 | semidirect |
| 142. C8 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D31 | 2 |
| #14521454 | 2 |
| #14521453 | 2 |
| #14521452 | 2 |
| #107×D31 | 2 |
| C4×C8×D31 | 2 |
| C31×#500 | 2 |
| C2×#500 | 31 |