Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521756 | C2 | semidirect |
| 2. #14521720 | C2 | semidirect |
| 3. #14521412 | C2 | semidirect |
| 4. #14521396 | C2 | semidirect |
| 5. #14521352 | C2 | semidirect |
| 6. #14521339 | C2 | semidirect |
| 7. #14521244 | C2 | semidirect |
| 8. #14521242 | C2 | semidirect |
| 9. #14521179 | C2 | semidirect |
| 10. #14521158 | C2 | semidirect |
| 11. C4×D8×C31 | C2 | semidirect |
| 80. D4×C31 | #41 | semidirect |
| 134. C4×D8 | D31 | semidirect |
| 170. C31 | #3366 | semidirect |
| 218. D4 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521756 | 2 |
| #14521720 | 2 |
| #14521412 | 2 |
| #14521396 | 2 |
| #14521352 | 2 |
| #14521339 | 2 |
| #14521244 | 2 |
| #14521242 | 2 |
| #14521179 | 2 |
| #14521158 | 2 |
| C4×D8×C31 | 2 |
| #3366 | 31 |