Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#11758489 | C2 | semidirect |
| 2. C2×D8×D31 | C2 | semidirect |
| 3. #14521483 | C2 | direct (N × H) |
| 4. C2×#11758388 | C2 | semidirect |
| 5. C2×#11758415 | C2 | semidirect |
| 6. C2×#11758414 | C2 | semidirect |
| 7. C2×#11758386 | C2 | semidirect |
| 8. C2×C31×D16 | C2 | semidirect |
| 12. C2×D8×C31 | C22 | semidirect |
| 16. #11758489 | C22 | semidirect |
| 18. D8×D31 | C22 | semidirect |
| 19. C2×Dic124 | C22 | semidirect |
| 22. C31×D16 | C22 | semidirect |
| 23. C2×C16×C31 | C22 | semidirect |
| 24. #11758415 | C22 | semidirect |
| 25. #11758414 | C22 | semidirect |
| 26. C2×C31⋊C16 | C22 | semidirect |
| 27. #11758388 | C22 | semidirect |
| 28. #11758386 | C22 | semidirect |
| 45. D8×C31 | C23 | semidirect |
| 51. Dic124 | C23 | semidirect |
| 56. C16×C31 | C23 | semidirect |
| 57. C31⋊C16 | C23 | semidirect |
| 104. C2×D16 | D31 | semidirect |
| 108. C2×C31 | #509 | semidirect |
| 123. C2×D8 | C2×D31 | semidirect |
| 128. D16 | C2×D31 | semidirect |
| 131. C2×C16 | C2×D31 | semidirect |
| 132. C31 | C2×#509 | semidirect |
| 155. D8 | C22×D31 | semidirect |
| 161. C16 | C22×D31 | semidirect |
| 205. C2 | #14521483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758489 | 2 |
| C2×D8×D31 | 2 |
| #14521483 | 2 |
| C2×#11758388 | 2 |
| C2×#11758415 | 2 |
| C2×#11758414 | 2 |
| C2×#11758386 | 2 |
| C2×C31×D16 | 2 |
| C2×#509 | 31 |