Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1088 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 261 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D31 |
| commutator | C22×C31 | C23×C4 |
| Fitting | C31×#379 | C2 |
| socle, cosocle | C23×C31 | C24 |
| prime radical | C25×C31 | C22 |
| hypercenter | #379 | D31 |
| hypocenter | C31 | #2280 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#11758454 | C2 | semidirect |
| 3. #14520910 | C2 | semidirect |
| 4. #14520907 | C2 | semidirect |
| 6. C22⋊C4×Dic31 | C2 | semidirect |
| 10. C23×Dic31 | C4 | semidirect |
| 19. C2×Dic31⋊C4 | C22 | semidirect |
| 20. C2×C4×Dic31 | C22 | semidirect |
| 22. C31⋊#95 | C22 | semidirect |
| 67. C2×Dic31 | C22⋊C4 | semidirect |
| 81. C22×C31 | #117 | semidirect |
| 117. C31 | #2280 | semidirect |
| 174. C22 | #11758454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic31 | 2 |
| C2×#11758454 | 2 |
| #14520910 | 2 |
| #14520907 | 2 |
| #14520905 | 2 |
| C22⋊C4×Dic31 | 2 |
| C31×#379 | 2 |
| #2280 | 31 |