Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D124 |
| commutator, cosocle | C4×C31 | C25 |
| Frattini | C4 | C24×D31 |
| Fitting | C31×#568 | C2 |
| socle | C2×C31 | C23×D4 |
| hypercenter | #568 | D31 |
| hypocenter | C31 | #3586 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14521885 | C2 | semidirect |
| 2. C2×#11758567 | C2 | semidirect |
| 3. #14521866 | C2 | semidirect |
| 4. #14521861 | C2 | semidirect |
| 5. #14521849 | C2 | semidirect |
| 6. C2×#11758486 | C2 | semidirect |
| 7. C31×#568 | C2 | semidirect |
| 10. #11758567 | C22 | semidirect |
| 11. #11758567 | C22 | semidirect |
| 12. #11758566 | C22 | semidirect |
| 19. C2×#92495 | C22 | semidirect |
| 20. C22×Dic62 | C22 | semidirect |
| 21. C31×#131 | C22 | semidirect |
| 22. C2×M16×C31 | C22 | semidirect |
| 23. #11758486 | C22 | semidirect |
| 24. #11758486 | C22 | semidirect |
| 25. #11758486 | C22 | semidirect |
| 26. #11758485 | C22 | semidirect |
| 27. #11758485 | C22 | semidirect |
| 28. C2×Dic124 | C22 | semidirect |
| 29. #11758481 | C22 | semidirect |
| 30. C2×#92470 | C22 | semidirect |
| 114. #568 | D31 | semidirect |
| 141. #131 | C2×D31 | semidirect |
| 142. C2×M16 | C2×D31 | semidirect |
| 143. C31 | #3586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521885 | 2 |
| C2×#11758567 | 2 |
| #14521866 | 2 |
| #14521861 | 2 |
| #14521849 | 2 |
| C2×#11758486 | 2 |
| C31×#568 | 2 |
| #3586 | 31 |