Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 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×#399 | C2 |
| prime radical | C24×D31 | C22 |
| hypercenter | #399 | D31 |
| hypocenter | C31 | #2842 |
| LCS | G ▷ C23×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14520985 | C2 | semidirect |
| 2. #14520973 | C2 | semidirect |
| 3. #14520971 | C2 | semidirect |
| 5. C31×#399 | C2 | semidirect |
| 7. C2×C4⋊C4×C31 | C22 | semidirect |
| 12. C2×C4⋊Dic31 | C22 | semidirect |
| 13. C2×Dic31⋊C4 | C22 | semidirect |
| 14. C31×#95 | C22 | semidirect |
| 15. C31⋊#95 | C22 | semidirect |
| 63. #399 | D31 | semidirect |
| 75. C2×C4⋊C4 | C2×D31 | semidirect |
| 81. #95 | C2×D31 | semidirect |
| 82. C31 | #2842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14520985 | 2 |
| #14520973 | 2 |
| #14520971 | 2 |
| #14520904 | 2 |
| C31×#399 | 2 |
| #2842 | 31 |