Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521704 | C2 | semidirect |
| 2. #14521401 | C2 | semidirect |
| 3. #14521390 | C2 | semidirect |
| 4. #14521336 | C2 | semidirect |
| 5. #14521276 | C2 | semidirect |
| 6. #14521254 | C2 | semidirect |
| 7. #14521192 | C2 | semidirect |
| 8. C4×#92479 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. #14521043 | C2 | semidirect |
| 11. C31×#555 | C2 | semidirect |
| 125. #555 | D31 | semidirect |
| 171. C31 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521704 | 2 |
| #14521401 | 2 |
| #14521390 | 2 |
| #14521336 | 2 |
| #14521276 | 2 |
| #14521254 | 2 |
| #14521192 | 2 |
| C4×#92479 | 2 |
| D4×C31⋊C8 | 2 |
| #14521043 | 2 |
| C31×#555 | 2 |
| #3303 | 31 |