Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758567 | C2 | semidirect |
| 2. C2×#11758509 | C2 | semidirect |
| 3. C2×#11758513 | C2 | semidirect |
| 4. #14521220 | C2 | direct (N × H) |
| 5. C2×#11758425 | C2 | semidirect |
| 6. C2×#11758413 | C2 | semidirect |
| 7. C2×#11758412 | C2 | semidirect |
| 8. C2×C31×AGL(1,ℤ/8) | C2 | semidirect |
| 14. #11758567 | C22 | semidirect |
| 23. C31×AGL(1,ℤ/8) | C22 | semidirect |
| 29. #11758513 | C22 | semidirect |
| 32. #11758509 | C22 | semidirect |
| 36. #11758425 | C22 | semidirect |
| 37. #11758413 | C22 | semidirect |
| 38. #11758412 | C22 | semidirect |
| 171. C2×AGL(1,ℤ/8) | D31 | semidirect |
| 181. C2×C31 | #454 | semidirect |
| 200. AGL(1,ℤ/8) | C2×D31 | semidirect |
| 214. C31 | C2×#454 | semidirect |
| 349. C2 | #14521220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758567 | 2 |
| C2×#11758509 | 2 |
| C2×#11758513 | 2 |
| #14521220 | 2 |
| C2×#11758425 | 2 |
| C2×#11758413 | 2 |
| C2×#11758412 | 2 |
| C2×C31×AGL(1,ℤ/8) | 2 |
| C2×#454 | 31 |