Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521604 | C2 | semidirect |
| 3. #14521412 | C2 | semidirect |
| 4. #14521397 | C2 | semidirect |
| 5. #14521396 | C2 | semidirect |
| 6. #14521395 | C2 | semidirect |
| 7. #14521052 | C2 | semidirect |
| 8. C4×#92469 | C2 | semidirect |
| 9. C31×#486 | C2 | semidirect |
| 13. C31×C4⋊Q8 | C22 | semidirect |
| 23. #11758467 | C22 | semidirect |
| 27. #11758446 | C22 | semidirect |
| 28. C31×#102 | C22 | semidirect |
| 29. C4×C8×C31 | C22 | semidirect |
| 30. #11758420 | C22 | semidirect |
| 31. #11758409 | C22 | semidirect |
| 32. #11758403 | C22 | semidirect |
| 33. #11758397 | C22 | semidirect |
| 34. C4×C31⋊C8 | C22 | semidirect |
| 124. #486 | D31 | semidirect |
| 138. C4⋊Q8 | C2×D31 | semidirect |
| 154. #102 | C2×D31 | semidirect |
| 157. C4×C8 | C2×D31 | semidirect |
| 158. C31 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521604 | 2 |
| #127×D31 | 2 |
| #14521412 | 2 |
| #14521397 | 2 |
| #14521396 | 2 |
| #14521395 | 2 |
| #14521052 | 2 |
| C4×#92469 | 2 |
| C31×#486 | 2 |
| #3138 | 31 |