Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 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. #14521854 | C2 | semidirect |
| 2. #14521851 | C2 | semidirect |
| 3. #14521426 | C2 | semidirect |
| 4. #14521320 | C2 | semidirect |
| 5. #14521319 | C2 | semidirect |
| 6. #14521218 | C2 | semidirect |
| 7. #14521167 | C2 | semidirect |
| 8. C31×#443 | C2 | semidirect |
| 9. #11758566 | C22 | semidirect |
| 11. C31×#131 | C22 | semidirect |
| 12. #11758526 | C22 | semidirect |
| 17. #11758485 | C22 | semidirect |
| 21. C2×D248 | C22 | semidirect |
| 22. C2×D248 | C22 | semidirect |
| 23. #11758478 | C22 | semidirect |
| 24. #11758451 | C22 | semidirect |
| 25. C31×#108 | C22 | semidirect |
| 26. C31×#104 | C22 | semidirect |
| 27. C4×C8×C31 | C22 | semidirect |
| 28. #11758411 | C22 | semidirect |
| 29. #11758407 | C22 | semidirect |
| 30. #11758393 | C22 | semidirect |
| 40. Q16×C31 | D4 | semidirect |
| 41. SD16×C31 | D4 | semidirect |
| 42. D8×C31 | D4 | semidirect |
| 52. Dic124 | D4 | semidirect |
| 58. D248 | D4 | semidirect |
| 60. #92470 | D4 | semidirect |
| 106. #443 | D31 | semidirect |
| 126. #131 | C2×D31 | semidirect |
| 129. #108 | C2×D31 | semidirect |
| 131. #104 | C2×D31 | semidirect |
| 133. C4×C8 | C2×D31 | semidirect |
| 134. C31 | #3292 | semidirect |
| 145. Q16 | D124 | semidirect |
| 149. SD16 | D124 | semidirect |
| 157. D8 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521854 | 2 |
| #14521851 | 2 |
| #14521426 | 2 |
| #14521320 | 2 |
| #14521319 | 2 |
| #14521218 | 2 |
| #14521167 | 2 |
| C31×#443 | 2 |
| #3292 | 31 |