Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1232 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Fitting | C7×#6893 | C3 |
| hypercenter | #6893 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6893 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6893 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×ΓL(1,𝔽8)×3−1+2 | C3 | semidirect |
| 3. C32×C9×ΓL(1,𝔽8) | C3 | semidirect |
| 4. #13133557 | C3 | semidirect |
| 5. #13133556 | C3 | semidirect |
| 6. #13133555 | C3 | semidirect |
| 7. #13133554 | C3 | semidirect |
| 8. ΓL(1,𝔽8)×C32⋊C9 | C3 | semidirect |
| 9. C7×#6893 | C3 | semidirect |
| 13. C3×C7×3−1+2 | C32 | semidirect |
| 15. C32×C7×C9 | C32 | semidirect |
| 18. C3×#4430 | C32 | semidirect |
| 19. C32×C7⋊C9 | C32 | semidirect |
| 22. C3×#4428 | C32 | semidirect |
| 23. C3×#4427 | C32 | semidirect |
| 27. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 28. C7×C32⋊C9 | C32 | semidirect |
| 29. C32⋊(C7⋊C9) | C32 | semidirect |
| 30. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 31. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 39. #6893 | ΓL(1,𝔽8) | direct (N × H) |
| 72. C3×3−1+2 | C3×ΓL(1,𝔽8) | semidirect |
| 82. C32×C9 | C3×ΓL(1,𝔽8) | semidirect |
| 86. C32⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 135. ΓL(1,𝔽8) | #6893 | direct (N × H) |
| 153. C7 | C3×#6893 | semidirect |