Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C22×#92482 | C2 | semidirect |
| 5. #14521323 | C2 | direct (N × H) |
| 6. C2×#11758410 | C2 | semidirect |
| 7. C2×#11758412 | C2 | semidirect |
| 8. C2×C31×#101 | C2 | semidirect |
| 18. C2×#92482 | C22 | semidirect |
| 32. C31×#101 | C22 | semidirect |
| 33. #11758412 | C22 | semidirect |
| 34. #11758410 | C22 | semidirect |
| 136. C2×#101 | D31 | semidirect |
| 139. C2×C31 | #473 | semidirect |
| 167. #101 | C2×D31 | semidirect |
| 168. C31 | C2×#473 | semidirect |
| 265. C2 | #14521323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758486 | 2 |
| C2×#11758519 | 2 |
| C22×#92482 | 2 |
| C2×#11758484 | 2 |
| #14521323 | 2 |
| C2×#11758410 | 2 |
| C2×#11758412 | 2 |
| C2×C31×#101 | 2 |
| C2×#473 | 31 |