Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1232 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 310 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C33 | C32×ΓL(1,𝔽8) |
| commutator | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C3×C7×C32⋊C9 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C3×C32⋊C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6893 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C3×C32⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#4427 | C3 | semidirect |
| 2. C32×#4428 | C3 | semidirect |
| 4. C32×C9×ΓL(1,𝔽8) | C3 | semidirect |
| 5. #13133555 | C3 | direct (N × H) |
| 6. C3×C32⋊(C7⋊C9) | C3 | semidirect |
| 7. C3×(C3×ΓL(1,𝔽8))⋊C9 | C3 | semidirect |
| 8. C3×(C3×ΓL(1,𝔽8))⋊C9 | C3 | semidirect |
| 9. C3×(C3×ΓL(1,𝔽8))⋊C9 | C3 | semidirect |
| 10. C3×C7×C32⋊C9 | C3 | semidirect |
| 24. C3×#4428 | C32 | semidirect |
| 26. C3×#4427 | C32 | semidirect |
| 28. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 29. C7×C32⋊C9 | C32 | semidirect |
| 30. C32⋊(C7⋊C9) | C32 | semidirect |
| 31. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 32. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 33. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 43. C3×C32⋊C9 | ΓL(1,𝔽8) | semidirect |
| 94. C32⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 147. C3×C7 | #6893 | semidirect |
| 175. C7 | C3×#6893 | semidirect |
| 179. C3 | #13133555 | direct (N × H) |