Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14521160 | C2 | semidirect |
| 4. #14521131 | C2 | semidirect |
| 5. #14521053 | C2 | semidirect |
| 6. #14521004 | C2 | semidirect |
| 7. C31×#427 | C2 | semidirect |
| 13. C2×D248 | C4 | semidirect |
| 16. #11758470 | C22 | semidirect |
| 19. C31×#107 | C22 | semidirect |
| 20. C31×#106 | C22 | semidirect |
| 21. #11758403 | C22 | semidirect |
| 22. C8×Dic31 | C22 | semidirect |
| 23. #11758397 | C22 | semidirect |
| 28. C2×D124 | C2×C4 | semidirect |
| 31. C2×C8×C31 | C2×C4 | semidirect |
| 43. D248 | C2×C4 | semidirect |
| 44. D248 | C2×C4 | semidirect |
| 78. #427 | D31 | semidirect |
| 96. #107 | C2×D31 | semidirect |
| 97. #106 | C2×D31 | semidirect |
| 101. C31 | #2948 | semidirect |
| 113. 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 |
| #14521160 | 2 |
| #14521131 | 2 |
| #14521053 | 2 |
| #14521004 | 2 |
| C31×#427 | 2 |
| #2948 | 31 |