Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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, socle, cosocle | C23×C31 | C24 |
| Fitting | C31×#393 | C2 |
| prime radical | C24×D31 | C22 |
| hypercenter | #393 | D31 |
| hypocenter | C31 | #2840 |
| LCS | G ▷ C23×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14520962 | C2 | semidirect |
| 2. #14520961 | C2 | semidirect |
| 3. #14520960 | C2 | semidirect |
| 5. C31×#393 | C2 | semidirect |
| 7. C22×Q8×C31 | C22 | semidirect |
| 8. C22×Dic62 | C22 | semidirect |
| 13. C31×#95 | C22 | semidirect |
| 14. C31⋊#95 | C22 | semidirect |
| 15. C31⋊#95 | C22 | semidirect |
| 19. C23×D31 | Q8 | semidirect |
| 67. #393 | D31 | semidirect |
| 76. C22×Q8 | C2×D31 | semidirect |
| 83. #95 | C2×D31 | semidirect |
| 84. C31 | #2840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14520962 | 2 |
| #14520961 | 2 |
| #14520960 | 2 |
| #14520904 | 2 |
| C31×#393 | 2 |
| #2840 | 31 |