Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic31 | C2 | semidirect |
| 3. #14521363 | C2 | direct (N × H) |
| 4. C2×#11758406 | C2 | semidirect |
| 5. C2×#11758409 | C2 | semidirect |
| 6. C2×C31×C22⋊C8 | C2 | semidirect |
| 19. C2×C4⋊Dic31 | C22 | semidirect |
| 20. C31×C22⋊C8 | C22 | semidirect |
| 21. #11758409 | C22 | semidirect |
| 22. #11758406 | C22 | semidirect |
| 95. C2×C22⋊C8 | D31 | semidirect |
| 97. C2×C31 | #480 | semidirect |
| 117. C22⋊C8 | C2×D31 | semidirect |
| 118. C31 | C2×#480 | semidirect |
| 187. C2 | #14521363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758507 | 2 |
| C22×C4⋊Dic31 | 2 |
| #14521363 | 2 |
| C2×#11758406 | 2 |
| C2×#11758409 | 2 |
| C2×C31×C22⋊C8 | 2 |
| C2×#480 | 31 |