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×C22⋊D31 |
| commutator, cosocle | C4×C31 | C25 |
| Frattini | C4 | C24×D31 |
| Fitting | C31×#585 | C2 |
| socle | C2×C31 | C23×D4 |
| hypercenter | #585 | D31 |
| hypocenter | C31 | #3586 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758567 | C2 | semidirect |
| 2. #14521864 | C2 | semidirect |
| 3. #14521860 | C2 | semidirect |
| 4. #14521847 | C2 | semidirect |
| 5. C2×#11758528 | C2 | semidirect |
| 6. #14521816 | C2 | semidirect |
| 7. C31×#585 | C2 | semidirect |
| 9. C31×2−1+4 | C22 | semidirect |
| 11. C31×H(5,𝔽2) | C22 | semidirect |
| 16. #11758567 | C22 | semidirect |
| 19. C2×#92495 | C22 | semidirect |
| 20. C22×Dic62 | C22 | semidirect |
| 21. #11758528 | C22 | semidirect |
| 22. #11758528 | C22 | semidirect |
| 23. #11758527 | C22 | semidirect |
| 24. #11758526 | C22 | semidirect |
| 25. #11758525 | C22 | semidirect |
| 26. C2×#92482 | C22 | semidirect |
| 27. #11758519 | C22 | semidirect |
| 28. C2×#92480 | C22 | semidirect |
| 29. #11758509 | C22 | semidirect |
| 30. C2×#92474 | C22 | semidirect |
| 108. #585 | D31 | semidirect |
| 123. 2−1+4 | C2×D31 | semidirect |
| 125. H(5,𝔽2) | 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 |
|---|---|
| C2×#11758567 | 2 |
| #14521864 | 2 |
| #14521860 | 2 |
| #14521847 | 2 |
| C2×#11758528 | 2 |
| #14521816 | 2 |
| C31×#585 | 2 |
| #3586 | 31 |