Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 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 | C2×H(3,𝔽4) |
| 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. #14521792 | C2 | semidirect |
| 2. #14521791 | C2 | semidirect |
| 3. #124×D31 | C2 | semidirect |
| 4. #120×D31 | C2 | semidirect |
| 5. C31×H(3,𝔽4) | C2 | semidirect |
| 6. C24×D31 | C22 | semidirect |
| 7. C2×Q8×D31 | C22 | semidirect |
| 9. C31×#124 | C22 | semidirect |
| 10. C31×#120 | C22 | semidirect |
| 11. #11758530 | C22 | semidirect |
| 12. #11758524 | C22 | semidirect |
| 13. #11758514 | C22 | semidirect |
| 14. #11758513 | C22 | semidirect |
| 15. #11758462 | C22 | semidirect |
| 16. #11758459 | C22 | semidirect |
| 17. C22⋊C4×D31 | C22 | semidirect |
| 18. #11758452 | C22 | semidirect |
| 19. C42×D31 | C22 | semidirect |
| 20. C24×C31 | C23 | semidirect |
| 23. C23×D31 | C23 | semidirect |
| 24. C2×Q8×C31 | C23 | semidirect |
| 31. C2×Dic62 | C23 | semidirect |
| 32. C22⋊C4×C31 | C23 | semidirect |
| 33. C42×C31 | C23 | semidirect |
| 34. C22⋊Dic31 | C23 | semidirect |
| 35. (C2×D31)⋊C4 | C23 | semidirect |
| 36. C4×Dic31 | C23 | semidirect |
| 64. H(3,𝔽4) | D31 | direct (N × H) |
| 70. D31 | H(3,𝔽4) | direct (N × H) |
| 78. #124 | C2×D31 | semidirect |
| 82. #120 | C2×D31 | semidirect |
| 85. C31 | C2×H(3,𝔽4) | semidirect |
| 89. C24 | C22×D31 | semidirect |
| 92. C2×Q8 | C22×D31 | semidirect |
| 100. C22⋊C4 | C22×D31 | semidirect |
| 102. C42 | C22×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521792 | 2 |
| #14521791 | 2 |
| #124×D31 | 2 |
| #120×D31 | 2 |
| C31×H(3,𝔽4) | 2 |
| C2×H(3,𝔽4) | 31 |