Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14521604 | C2 | semidirect |
| 3. #14521355 | C2 | semidirect |
| 4. #14521347 | C2 | semidirect |
| 5. #14521345 | C2 | semidirect |
| 6. #14521339 | C2 | semidirect |
| 7. #14521331 | C2 | semidirect |
| 8. #14521086 | C2 | semidirect |
| 9. C4⋊C8×D31 | C2 | semidirect |
| 11. C31×#474 | C2 | semidirect |
| 50. #92497 | Q8 | semidirect |
| 137. #474 | D31 | semidirect |
| 177. C31 | #3076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521604 | 2 |
| C4×#92497 | 2 |
| #14521355 | 2 |
| #14521347 | 2 |
| #14521345 | 2 |
| #14521339 | 2 |
| #14521331 | 2 |
| #14521086 | 2 |
| C4⋊C8×D31 | 2 |
| #14521042 | 2 |
| C31×#474 | 2 |
| #3076 | 31 |