Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D31 |
| commutator, socle, cosocle | C22×C31 | C25 |
| Fitting | C31×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D31 |
| hypocenter | C31 | #3529 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14521799 | C2 | semidirect |
| 2. #14521793 | C2 | semidirect |
| 3. #14521788 | C2 | semidirect |
| 4. #14521598 | C2 | semidirect |
| 5. #14521578 | C2 | semidirect |
| 6. #14521555 | C2 | semidirect |
| 7. C31×H(3,𝔽4) | C2 | semidirect |
| 8. C23×Dic31 | C22 | semidirect |
| 9. C2×#92499 | C22 | semidirect |
| 14. #11758530 | C22 | semidirect |
| 15. #11758523 | C22 | semidirect |
| 16. Q8×Dic31 | C22 | semidirect |
| 17. #11758521 | C22 | semidirect |
| 23. #11758463 | C22 | semidirect |
| 24. #11758461 | C22 | semidirect |
| 25. #11758460 | C22 | semidirect |
| 26. (C22⋊D31)⋊C4 | C22 | semidirect |
| 27. #11758456 | C22 | semidirect |
| 28. #11758455 | C22 | semidirect |
| 29. #11758454 | C22 | semidirect |
| 30. #11758452 | C22 | semidirect |
| 31. C42×D31 | C22 | semidirect |
| 32. #11758447 | C22 | semidirect |
| 96. H(3,𝔽4) | D31 | semidirect |
| 130. C31 | #3529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521799 | 2 |
| #14521793 | 2 |
| #14521788 | 2 |
| #14521598 | 2 |
| #14521578 | 2 |
| #14521555 | 2 |
| C31×H(3,𝔽4) | 2 |
| #3529 | 31 |