Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #14521532 | C2 | semidirect |
| 3. #14521055 | C2 | semidirect |
| 4. #14521051 | C2 | semidirect |
| 5. #14521046 | C2 | semidirect |
| 6. C2×#11758409 | C2 | semidirect |
| 7. C2×C31×#131 | C2 | semidirect |
| 10. #11758566 | C4 | semidirect |
| 16. C2×M16×C31 | C22 | semidirect |
| 17. C22×C8×C31 | C22 | semidirect |
| 20. #11758503 | C22 | semidirect |
| 21. C2×C4⋊Dic31 | C22 | semidirect |
| 22. #11758409 | C22 | semidirect |
| 23. #11758409 | C22 | semidirect |
| 24. #11758409 | C22 | semidirect |
| 25. #11758404 | C22 | semidirect |
| 26. #11758404 | C22 | semidirect |
| 38. #92495 | C2×C4 | semidirect |
| 41. C2×D124 | C2×C4 | semidirect |
| 94. C2×#131 | D31 | semidirect |
| 113. C2×M16 | C2×D31 | semidirect |
| 114. C22×C8 | C2×D31 | semidirect |
| 124. C31 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758566 | 2 |
| #14521532 | 2 |
| #14521055 | 2 |
| #14521051 | 2 |
| #14521046 | 2 |
| C2×#11758409 | 2 |
| C2×C31×#131 | 2 |
| #2897 | 31 |