Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.
This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C13⋊C3 |
| commutator, socle, cosocle | C3×C13 | C35 |
| Fitting | C13×3−1+4 | C3 |
| prime radical | C13⋊H(5,𝔽3) | C3 |
| hypercenter | 3−1+4 | C13⋊C3 |
| hypocenter | C13 | #10624943 |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C3 ◁ 3−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15691698 | C3 | semidirect |
| 2. #15691697 | C3 | semidirect |
| 3. #15691696 | C3 | semidirect |
| 4. #15691695 | C3 | semidirect |
| 6. C3×#11760454 | C3 | semidirect |
| 7. C3×#11760452 | C3 | semidirect |
| 8. C13⋊C3×#737 | C3 | semidirect |
| 9. C13×3−1+4 | C3 | semidirect |
| 10. #11760454 | C32 | semidirect |
| 11. #11760454 | C32 | semidirect |
| 12. #11760454 | C32 | semidirect |
| 13. #11760454 | C32 | semidirect |
| 14. #11760454 | C32 | semidirect |
| 15. #11760454 | C32 | semidirect |
| 16. #11760453 | C32 | semidirect |
| 17. #11760452 | C32 | semidirect |
| 18. #11760452 | C32 | semidirect |
| 19. #11760452 | C32 | semidirect |
| 20. #11760452 | C32 | semidirect |
| 21. C3×#66851 | C32 | semidirect |
| 22. C3×#66851 | C32 | semidirect |
| 23. C3×#66848 | C32 | semidirect |
| 24. C3×#66849 | C32 | semidirect |
| 25. 3−1+2×C13⋊C3 | C32 | semidirect |
| 28. C32×C13⋊C9 | C32 | semidirect |
| 29. C3×C9×C13⋊C3 | C32 | semidirect |
| 30. C13×#737 | C32 | semidirect |
| 31. C3×C13×3−1+2 | C32 | semidirect |
| 61. 3−1+4 | C13⋊C3 | semidirect |
| 88. #737 | C3×C13⋊C3 | semidirect |
| 94. C3×3−1+2 | C3×C13⋊C3 | semidirect |
| 127. C13 | #10624943 | semidirect |