Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1232 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 328 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 | C32×C7×3−1+2 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C32×3−1+2 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6893 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C32×3−1+2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#4430 | C3 | semidirect |
| 3. C33×C7⋊C9 | C3 | semidirect |
| 4. #13133557 | C3 | direct (N × H) |
| 5. C3×(C3×ΓL(1,𝔽8))⋊C9 | C3 | semidirect |
| 6. C32×C7×3−1+2 | C3 | semidirect |
| 11. C3×C7×3−1+2 | C32 | semidirect |
| 16. C3×#4430 | C32 | semidirect |
| 20. C32×C7⋊C9 | C32 | semidirect |
| 21. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 23. C32×3−1+2 | ΓL(1,𝔽8) | semidirect |
| 50. C3×3−1+2 | C3×ΓL(1,𝔽8) | semidirect |
| 89. C3×C7 | #6893 | semidirect |
| 105. C7 | C3×#6893 | semidirect |
| 108. C3 | #13133557 | direct (N × H) |