Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14521456 | C2 | semidirect |
| 4. #14521454 | C2 | semidirect |
| 5. #14521452 | C2 | semidirect |
| 6. #14521445 | C2 | semidirect |
| 9. C31×#498 | C2 | semidirect |
| 65. #92469 | Q8 | semidirect |
| 86. C8×C31 | C2×Q8 | semidirect |
| 87. C31⋊C8 | C2×Q8 | semidirect |
| 109. #498 | D31 | semidirect |
| 141. C31 | #3165 | semidirect |
| 194. C8 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521604 | 2 |
| C4⋊Q8×D31 | 2 |
| #14521456 | 2 |
| #14521454 | 2 |
| #14521452 | 2 |
| #14521445 | 2 |
| #14521088 | 2 |
| C4×#92469 | 2 |
| C31×#498 | 2 |
| #3165 | 31 |