Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11758526 | C2 | semidirect |
| 2. C2×#11758526 | C2 | semidirect |
| 3. #14521816 | C2 | semidirect |
| 4. #14521317 | C2 | semidirect |
| 5. #14521314 | C2 | semidirect |
| 6. #14521097 | C2 | semidirect |
| 7. #14521033 | C2 | semidirect |
| 8. C2×#11758411 | C2 | semidirect |
| 9. C31×#575 | C2 | semidirect |
| 14. C31×#137 | C22 | semidirect |
| 16. C31×AGL(1,ℤ/8) | C22 | semidirect |
| 24. #11758525 | C22 | semidirect |
| 26. C2×#92481 | C22 | semidirect |
| 28. C2×#92479 | C22 | semidirect |
| 33. #11758424 | C22 | semidirect |
| 34. #11758421 | C22 | semidirect |
| 35. #11758411 | C22 | semidirect |
| 36. #11758410 | C22 | semidirect |
| 141. #575 | D31 | semidirect |
| 161. #137 | C2×D31 | semidirect |
| 167. AGL(1,ℤ/8) | C2×D31 | semidirect |
| 184. C31 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758526 | 2 |
| #14521816 | 2 |
| #14521317 | 2 |
| #14521314 | 2 |
| #14521097 | 2 |
| #14521033 | 2 |
| C2×#11758411 | 2 |
| C31×#575 | 2 |
| #3068 | 31 |