Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14521850 | C2 | semidirect |
| 2. #14521485 | C2 | semidirect |
| 3. #14521483 | C2 | semidirect |
| 4. #14521481 | C2 | semidirect |
| 5. #14521478 | C2 | semidirect |
| 6. D16×D31 | C2 | semidirect |
| 7. #14521465 | C2 | semidirect |
| 8. C2×C31×D16 | C2 | semidirect |
| 10. C2×D8×C31 | C22 | semidirect |
| 12. #11758489 | C22 | semidirect |
| 14. D8×D31 | C22 | semidirect |
| 15. #11758481 | C22 | semidirect |
| 17. C31×D16 | C22 | semidirect |
| 18. C31×D16 | C22 | semidirect |
| 19. C2×C16×C31 | C22 | semidirect |
| 20. #11758415 | C22 | semidirect |
| 21. #11758414 | C22 | semidirect |
| 22. #11758400 | C22 | semidirect |
| 23. Dic248 | C22 | semidirect |
| 24. #11758388 | C22 | semidirect |
| 25. D496 | C22 | semidirect |
| 26. #11758386 | C22 | semidirect |
| 27. C16×D31 | C22 | semidirect |
| 86. C2×D16 | D31 | semidirect |
| 99. C2×D8 | C2×D31 | semidirect |
| 106. D16 | C2×D31 | semidirect |
| 107. D16 | C2×D31 | semidirect |
| 111. C2×C16 | C2×D31 | semidirect |
| 112. C31 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521850 | 2 |
| #14521485 | 2 |
| #14521483 | 2 |
| #14521481 | 2 |
| #14521478 | 2 |
| D16×D31 | 2 |
| #14521465 | 2 |
| C2×C31×D16 | 2 |
| #3415 | 31 |