Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#11758525 | C2 | semidirect |
| 2. #14521171 | C2 | semidirect |
| 3. #14521166 | C2 | semidirect |
| 4. #14521098 | C2 | semidirect |
| 5. #14521066 | C2 | semidirect |
| 6. #14521007 | C2 | semidirect |
| 9. C31×#137 | C4 | semidirect |
| 10. C31×AGL(1,ℤ/8) | C4 | semidirect |
| 15. #11758525 | C22 | semidirect |
| 16. #11758525 | C22 | semidirect |
| 22. #11758425 | C22 | semidirect |
| 23. #11758407 | C22 | semidirect |
| 24. #11758403 | C22 | semidirect |
| 25. C8×Dic31 | C22 | semidirect |
| 98. #137 | Dic31 | semidirect |
| 99. AGL(1,ℤ/8) | Dic31 | semidirect |
| 115. C31 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758525 | 2 |
| #14521171 | 2 |
| #14521166 | 2 |
| #14521098 | 2 |
| #14521066 | 2 |
| #14521007 | 2 |
| C31×#575 | 2 |
| #2955 | 31 |