Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #14521128 | C2 | semidirect |
| 3. #14521126 | C2 | semidirect |
| 4. #14521102 | C2 | semidirect |
| 5. #14521011 | C2 | semidirect |
| 6. C31×#431 | C2 | semidirect |
| 12. C2×#92469 | C22 | semidirect |
| 17. C31×C4⋊C8 | C22 | semidirect |
| 19. C4×C8×C31 | C22 | semidirect |
| 21. (C2×D31)⋊C8 | C22 | semidirect |
| 22. C4⋊(C31⋊C8) | C22 | semidirect |
| 23. C4×C31⋊C8 | C22 | semidirect |
| 53. C2×C4×C31 | M16 | semidirect |
| 88. #431 | D31 | semidirect |
| 106. C4⋊C8 | C2×D31 | semidirect |
| 111. C4×C8 | C2×D31 | semidirect |
| 112. C31 | #2975 | semidirect |
| 148. C2×C4 | #92469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| #14521128 | 2 |
| #14521126 | 2 |
| #14521102 | 2 |
| #14521011 | 2 |
| C31×#431 | 2 |
| #2975 | 31 |