Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11758527 | C2 | semidirect |
| 2. #14521599 | C2 | semidirect |
| 3. #14521431 | C2 | semidirect |
| 4. #14521428 | C2 | semidirect |
| 5. #14521425 | C2 | semidirect |
| 6. #14521423 | C2 | semidirect |
| 7. #14521421 | C2 | semidirect |
| 8. C2×C4×C31⋊C8 | C2 | semidirect |
| 9. C31×#532 | C2 | semidirect |
| 57. C2×C31⋊C8 | D4 | semidirect |
| 94. C4×C31 | #135 | semidirect |
| 99. #532 | D31 | semidirect |
| 133. C31 | #3147 | semidirect |
| 196. C4 | #11758527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758527 | 2 |
| #14521599 | 2 |
| #14521431 | 2 |
| #14521428 | 2 |
| #14521425 | 2 |
| #14521423 | 2 |
| #14521421 | 2 |
| C2×C4×C31⋊C8 | 2 |
| C31×#532 | 2 |
| #3147 | 31 |