Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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 |
|---|---|---|
| 3. #14520812 | C2 | semidirect |
| 4. #14520811 | C2 | semidirect |
| 5. C31×#340 | C2 | semidirect |
| 14. C2×C8×D31 | C4 | semidirect |
| 16. C4⋊C4×D31 | C4 | semidirect |
| 30. C2×C8×C31 | C2×C4 | semidirect |
| 32. C4⋊C4×C31 | C2×C4 | semidirect |
| 34. C4⋊Dic31 | C2×C4 | semidirect |
| 37. C2×C31⋊C8 | C2×C4 | semidirect |
| 84. #340 | D31 | direct (N × H) |
| 90. D31 | #340 | direct (N × H) |
| 102. C31 | C2×#340 | semidirect |
| 119. C2×C8 | C4×D31 | semidirect |
| 124. C4⋊C4 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D31 | 2 |
| C2×C4⋊C4×D31 | 2 |
| #14520812 | 2 |
| #14520811 | 2 |
| C31×#340 | 2 |
| C2×#340 | 31 |