Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #14521101 | C2 | semidirect |
| 3. #14521071 | C2 | semidirect |
| 4. #14520793 | C2 | semidirect |
| 5. #14520792 | C2 | semidirect |
| 6. #14520792 | C2 | semidirect |
| 7. C31×#331 | C2 | semidirect |
| 18. C31×C4⋊C8 | C22 | semidirect |
| 19. C31×C4⋊C8 | C22 | semidirect |
| 23. C4⋊(C31⋊C8) | C22 | semidirect |
| 24. C4⋊(C31⋊C8) | C22 | semidirect |
| 112. #331 | D31 | semidirect |
| 132. C4⋊C8 | C2×D31 | semidirect |
| 133. C4⋊C8 | C2×D31 | semidirect |
| 136. C31 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D31 | 2 |
| #14521101 | 2 |
| #14521071 | 2 |
| #14520793 | 2 |
| #14520792 | 2 |
| C31×#331 | 2 |
| #1545 | 31 |