Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #14521863 | C2 | semidirect |
| 2. #14521861 | C2 | semidirect |
| 3. #14521851 | C2 | semidirect |
| 4. #14521433 | C2 | semidirect |
| 5. #14521325 | C2 | semidirect |
| 6. #14521320 | C2 | semidirect |
| 7. #14521312 | C2 | semidirect |
| 8. #14521228 | C2 | semidirect |
| 9. #14521223 | C2 | semidirect |
| 10. #14521167 | C2 | semidirect |
| 11. C31×#443 | C2 | semidirect |
| 12. #11758567 | C22 | semidirect |
| 15. C31×#131 | C22 | semidirect |
| 16. #11758528 | C22 | semidirect |
| 27. #11758485 | C22 | semidirect |
| 28. C2×Dic124 | C22 | semidirect |
| 33. C2×#92470 | C22 | semidirect |
| 35. #11758478 | C22 | semidirect |
| 36. #11758452 | C22 | semidirect |
| 37. C31×#108 | C22 | semidirect |
| 38. C31×#104 | C22 | semidirect |
| 39. C4×C8×C31 | C22 | semidirect |
| 40. #11758412 | C22 | semidirect |
| 41. #11758411 | C22 | semidirect |
| 42. #11758407 | C22 | semidirect |
| 44. #11758393 | C22 | semidirect |
| 154. #443 | D31 | semidirect |
| 184. #131 | C2×D31 | semidirect |
| 187. #108 | C2×D31 | semidirect |
| 190. #104 | C2×D31 | semidirect |
| 193. C4×C8 | C2×D31 | semidirect |
| 194. C31 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521863 | 2 |
| #14521861 | 2 |
| #14521851 | 2 |
| #14521433 | 2 |
| #14521325 | 2 |
| #14521320 | 2 |
| #14521312 | 2 |
| #14521228 | 2 |
| #14521223 | 2 |
| #14521167 | 2 |
| C31×#443 | 2 |
| #3290 | 31 |