Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #14521523 | C2 | semidirect |
| 3. #14521162 | C2 | semidirect |
| 4. C4×D248 | C2 | semidirect |
| 5. #14521087 | C2 | semidirect |
| 6. #14521055 | C2 | semidirect |
| 7. C31×#405 | C2 | semidirect |
| 13. C2×D248 | C4 | semidirect |
| 18. C4×D124 | C22 | semidirect |
| 19. C31×#97 | C22 | semidirect |
| 20. C4×C8×C31 | C22 | semidirect |
| 21. #11758409 | C22 | semidirect |
| 22. #11758406 | C22 | semidirect |
| 23. #11758405 | C22 | semidirect |
| 28. C2×D124 | C2×C4 | semidirect |
| 32. C2×C8×C31 | C2×C4 | semidirect |
| 43. D248 | C2×C4 | semidirect |
| 44. D248 | C2×C4 | semidirect |
| 80. #405 | D31 | semidirect |
| 99. #97 | C2×D31 | semidirect |
| 100. C4×C8 | C2×D31 | semidirect |
| 101. C31 | #2948 | semidirect |
| 112. C2×C8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| #14521523 | 2 |
| #14521162 | 2 |
| C4×D248 | 2 |
| #14521087 | 2 |
| #14521055 | 2 |
| C31×#405 | 2 |
| #2948 | 31 |