Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D31 | C2 | semidirect |
| 3. #14521345 | C2 | semidirect |
| 4. #14521341 | C2 | semidirect |
| 5. #14521339 | C2 | semidirect |
| 6. #14521333 | C2 | semidirect |
| 7. #14521327 | C2 | semidirect |
| 8. #14521088 | C2 | semidirect |
| 9. #14521071 | C2 | semidirect |
| 11. C31×#476 | C2 | semidirect |
| 51. #92497 | Q8 | semidirect |
| 86. D4×C31 | C2×Q8 | semidirect |
| 110. Dic62 | C2×Q8 | semidirect |
| 138. #476 | D31 | semidirect |
| 180. C31 | #3079 | semidirect |
| 229. D4 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D31 | 2 |
| C4×#92497 | 2 |
| #14521345 | 2 |
| #14521341 | 2 |
| #14521339 | 2 |
| #14521333 | 2 |
| #14521327 | 2 |
| #14521088 | 2 |
| #14521071 | 2 |
| #14521047 | 2 |
| C31×#476 | 2 |
| #3079 | 31 |