Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14521849 | C2 | semidirect |
| 2. C2×#11758485 | C2 | semidirect |
| 3. C2×#11758485 | C2 | semidirect |
| 4. #14521815 | C2 | semidirect |
| 5. #14521320 | C2 | semidirect |
| 6. #14521313 | C2 | semidirect |
| 7. #14521031 | C2 | semidirect |
| 8. C2×#11758411 | C2 | semidirect |
| 9. C31×#430 | C2 | semidirect |
| 18. #11758486 | C22 | semidirect |
| 24. #11758485 | C22 | semidirect |
| 29. C2×D248 | C22 | semidirect |
| 31. C2×#92470 | C22 | semidirect |
| 32. #11758478 | C22 | semidirect |
| 33. C31×#108 | C22 | semidirect |
| 34. #11758412 | C22 | semidirect |
| 35. #11758411 | C22 | semidirect |
| 36. #11758411 | C22 | semidirect |
| 147. #430 | D31 | semidirect |
| 180. #108 | C2×D31 | semidirect |
| 184. C31 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521849 | 2 |
| C2×#11758485 | 2 |
| #14521815 | 2 |
| #14521320 | 2 |
| #14521313 | 2 |
| #14521031 | 2 |
| C2×#11758411 | 2 |
| C31×#430 | 2 |
| #3068 | 31 |