Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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. C2×#11758493 | C2 | semidirect |
| 2. #14521597 | C2 | semidirect |
| 3. C4×#92499 | C2 | semidirect |
| 4. #14521269 | C2 | semidirect |
| 5. #14521263 | C2 | semidirect |
| 6. #14521259 | C2 | semidirect |
| 7. #14521255 | C2 | semidirect |
| 8. #14521241 | C2 | semidirect |
| 9. C4⋊C8×D31 | C2 | semidirect |
| 10. #14521042 | C2 | semidirect |
| 11. C31×#460 | C2 | semidirect |
| 51. #92499 | D4 | semidirect |
| 137. C4×C31 | #135 | semidirect |
| 152. #460 | D31 | semidirect |
| 194. C31 | #3035 | semidirect |
| 292. C4 | #11758493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758493 | 2 |
| #14521597 | 2 |
| C4×#92499 | 2 |
| #14521269 | 2 |
| #14521263 | 2 |
| #14521259 | 2 |
| #14521255 | 2 |
| #14521241 | 2 |
| C4⋊C8×D31 | 2 |
| #14521042 | 2 |
| C31×#460 | 2 |
| #3035 | 31 |