Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 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. C2×Q8×Dic31 | C2 | semidirect |
| 3. #14520955 | C2 | semidirect |
| 4. #14520954 | C2 | semidirect |
| 7. C2×C4×Q8×C31 | C2 | semidirect |
| 11. C2×Q8×D31 | C4 | semidirect |
| 45. (C2×D31)⋊C4 | Q8 | direct (N × H) |
| 56. Q8×C31 | C22⋊C4 | semidirect |
| 65. C2×C4×C31 | C2×Q8 | semidirect |
| 74. C2×Dic31 | C2×Q8 | semidirect |
| 91. C2×D31 | C4×Q8 | semidirect |
| 100. C2×C4×Q8 | D31 | semidirect |
| 130. C31 | Q8×C22⋊C4 | semidirect |
| 163. Q8 | (C2×D31)⋊C4 | direct (N × H) |
| 181. C2×C4 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D31 | 2 |
| C2×Q8×Dic31 | 2 |
| #14520955 | 2 |
| #14520954 | 2 |
| #14520906 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| C2×C4×Q8×C31 | 2 |
| Q8×C22⋊C4 | 31 |