Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#11758519 | C2 | semidirect |
| 3. C2×#11758521 | C2 | semidirect |
| 4. #14521230 | C2 | direct (N × H) |
| 5. C2×#11758425 | C2 | semidirect |
| 6. C2×#11758413 | C2 | semidirect |
| 7. C2×#11758412 | C2 | semidirect |
| 8. C2×C31×#137 | C2 | semidirect |
| 23. C31×#137 | C22 | semidirect |
| 28. #11758521 | C22 | semidirect |
| 31. #11758519 | C22 | semidirect |
| 36. #11758425 | C22 | semidirect |
| 37. #11758413 | C22 | semidirect |
| 38. #11758412 | C22 | semidirect |
| 167. C2×#137 | D31 | semidirect |
| 176. C2×C31 | #456 | semidirect |
| 195. #137 | C2×D31 | semidirect |
| 209. C31 | C2×#456 | semidirect |
| 339. C2 | #14521230 | 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×#11758519 | 2 |
| C2×#11758521 | 2 |
| #14521230 | 2 |
| C2×#11758425 | 2 |
| C2×#11758413 | 2 |
| C2×#11758412 | 2 |
| C2×C31×#137 | 2 |
| C2×#456 | 31 |