Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #14521885 | C2 | semidirect |
| 2. #14521864 | C2 | semidirect |
| 3. #14521857 | C2 | semidirect |
| 4. #14521847 | C2 | semidirect |
| 5. C2×#11758519 | C2 | semidirect |
| 6. #14521816 | C2 | semidirect |
| 7. C2×C31×2−1+4 | C2 | semidirect |
| 9. C31×2−1+4 | C22 | semidirect |
| 12. C2×#41×C31 | C22 | semidirect |
| 14. C22×Q8×C31 | C22 | semidirect |
| 15. #11758567 | C22 | semidirect |
| 16. #11758566 | C22 | semidirect |
| 21. #11758528 | C22 | semidirect |
| 22. #11758527 | C22 | semidirect |
| 23. #11758526 | C22 | semidirect |
| 24. #11758525 | C22 | semidirect |
| 25. C2×#92482 | C22 | semidirect |
| 26. #11758519 | C22 | semidirect |
| 27. #11758519 | C22 | semidirect |
| 28. C2×#92481 | C22 | semidirect |
| 29. #11758509 | C22 | semidirect |
| 30. C2×#92474 | C22 | semidirect |
| 109. C2×2−1+4 | D31 | semidirect |
| 123. 2−1+4 | C2×D31 | semidirect |
| 130. C2×#41 | C2×D31 | semidirect |
| 132. C22×Q8 | C2×D31 | semidirect |
| 143. C31 | #3586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521885 | 2 |
| #14521864 | 2 |
| #14521857 | 2 |
| #14521847 | 2 |
| C2×#11758519 | 2 |
| #14521816 | 2 |
| C2×C31×2−1+4 | 2 |
| #3586 | 31 |