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. #14521851 | C2 | semidirect |
| 2. #14521486 | C2 | semidirect |
| 3. #14521484 | C2 | semidirect |
| 4. #14521482 | C2 | semidirect |
| 5. C2×D496 | C2 | semidirect |
| 6. D16×D31 | C2 | semidirect |
| 7. #14521465 | C2 | semidirect |
| 8. C31×#508 | C2 | semidirect |
| 10. C31×#135 | C22 | semidirect |
| 12. #11758496 | C22 | semidirect |
| 14. D8×D31 | C22 | semidirect |
| 15. C2×D248 | C22 | semidirect |
| 17. C31×Q32 | C22 | semidirect |
| 18. C31×SD32 | C22 | semidirect |
| 19. C31×D16 | C22 | semidirect |
| 20. C2×C16×C31 | C22 | semidirect |
| 21. #11758416 | C22 | semidirect |
| 22. #11758414 | C22 | semidirect |
| 23. #11758400 | C22 | semidirect |
| 24. D496 | C22 | semidirect |
| 25. D496 | C22 | semidirect |
| 26. #11758386 | C22 | semidirect |
| 27. C16×D31 | C22 | semidirect |
| 84. #508 | D31 | semidirect |
| 97. #135 | C2×D31 | semidirect |
| 101. Q32 | C2×D31 | semidirect |
| 103. SD32 | 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 |
|---|---|
| #14521851 | 2 |
| #14521486 | 2 |
| #14521484 | 2 |
| #14521482 | 2 |
| C2×D496 | 2 |
| D16×D31 | 2 |
| #14521465 | 2 |
| C31×#508 | 2 |
| #3415 | 31 |