Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D31 |
| commutator, socle | C2×C31 | C23×C8 |
| Fitting | C31×#504 | C2 |
| prime radical | #41×D31 | C4 |
| cosocle | C8×C31 | C24 |
| hypercenter | #504 | D31 |
| hypocenter | C31 | #3407 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14521467 | C2 | semidirect |
| 3. #14521466 | C2 | semidirect |
| 4. #14521465 | C2 | semidirect |
| 5. C2×#11758386 | C2 | semidirect |
| 6. M32×D31 | C2 | semidirect |
| 7. C31×#504 | C2 | semidirect |
| 15. C31×M32 | C22 | semidirect |
| 16. C2×C16×C31 | C22 | semidirect |
| 17. #11758400 | C22 | semidirect |
| 18. C2×C31⋊C16 | C22 | semidirect |
| 21. #11758386 | C22 | semidirect |
| 22. #11758386 | C22 | semidirect |
| 23. C16×D31 | C22 | semidirect |
| 73. #504 | D31 | semidirect |
| 92. M32 | C2×D31 | semidirect |
| 95. C2×C16 | C2×D31 | semidirect |
| 96. C31 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D31 | 2 |
| #14521467 | 2 |
| #14521466 | 2 |
| #14521465 | 2 |
| C2×#11758386 | 2 |
| M32×D31 | 2 |
| C31×#504 | 2 |
| #3407 | 31 |