Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521583 | C2 | semidirect |
| 2. #14521455 | C2 | semidirect |
| 3. #14521436 | C2 | semidirect |
| 4. #14521413 | C2 | semidirect |
| 5. #14521411 | C2 | semidirect |
| 6. #14521300 | C2 | semidirect |
| 7. #14521293 | C2 | semidirect |
| 8. C4×#92480 | C2 | semidirect |
| 9. C4×#92479 | C2 | semidirect |
| 10. C4×#92474 | C2 | semidirect |
| 11. C31×#532 | C2 | semidirect |
| 110. C31⋊C8 | #41 | semidirect |
| 132. #532 | D31 | semidirect |
| 180. C31 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521583 | 2 |
| #14521455 | 2 |
| #14521436 | 2 |
| #14521413 | 2 |
| #14521411 | 2 |
| #14521300 | 2 |
| #14521293 | 2 |
| C4×#92480 | 2 |
| C4×#92479 | 2 |
| C4×#92474 | 2 |
| C31×#532 | 2 |
| #3171 | 31 |