Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C2×#11758415 | C2 | semidirect |
| 2. C22×C31⋊C16 | C2 | semidirect |
| 3. #14521290 | C2 | semidirect |
| 4. #14520876 | C2 | semidirect |
| 5. #14520852 | C2 | semidirect |
| 6. #14520850 | C2 | semidirect |
| 39. C31⋊C16 | D4 | semidirect |
| 63. C22×C31 | SD32 | semidirect |
| 96. C31 | #2217 | semidirect |
| 138. C22 | #11758415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758415 | 2 |
| C22×C31⋊C16 | 2 |
| #14521290 | 2 |
| #14520876 | 2 |
| #14520852 | 2 |
| #14520850 | 2 |
| C31×#466 | 2 |
| #2217 | 31 |