Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
788 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 788 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 | C3×C7×C9⋊C9 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C3×C9⋊C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6899 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C3×C9⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133592 | C3 | direct (N × H) |
| 3. C3×#10588036 | C3 | semidirect |
| 4. C3×#10588035 | C3 | semidirect |
| 5. C3×(C7⋊C9)⋊C9 | C3 | semidirect |
| 7. C3×C9×C7⋊C9 | C3 | semidirect |
| 8. C3×C7×C9⋊C9 | C3 | semidirect |
| 19. C7×C9⋊C9 | C32 | semidirect |
| 21. #10588036 | C32 | semidirect |
| 22. #10588035 | C32 | semidirect |
| 23. (C7⋊C9)⋊C9 | C32 | semidirect |
| 24. C9×C7⋊C9 | C32 | semidirect |
| 30. C3×C9⋊C9 | ΓL(1,𝔽8) | semidirect |
| 62. C9⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 94. C3×C7 | #6899 | semidirect |
| 110. C7 | C3×#6899 | semidirect |
| 112. C3 | #13133592 | direct (N × H) |