Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11758406 | C2 | semidirect |
| 3. C2×#11758395 | C2 | semidirect |
| 6. #14520811 | C2 | semidirect |
| 7. C31×#340 | C2 | semidirect |
| 21. (C2×D31)⋊C8 | C4 | semidirect |
| 42. C2×C8×C31 | C2×C4 | semidirect |
| 55. C2×C31⋊C8 | C2×C4 | semidirect |
| 106. C2×D31 | #107 | semidirect |
| 122. #340 | D31 | semidirect |
| 147. C31 | #1852 | semidirect |
| 169. C2×C8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D31 | 2 |
| C2×#11758406 | 2 |
| C2×#11758395 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| #14520906 | 2 |
| #14520811 | 2 |
| C31×#340 | 2 |
| #1852 | 31 |