Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
824 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 824 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 | C3×C9 | C32×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C33×C7×C9 | C3 |
| hypercenter | C33×C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624872 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C3×C9 ◁ C33×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13133570 | C3 | semidirect |
| 2. #13133564 | C3 | semidirect |
| 3. #13133563 | C3 | semidirect |
| 5. C9×#4430 | C3 | semidirect |
| 6. #13133530 | C3 | semidirect |
| 19. #10588036 | C32 | semidirect |
| 20. #10588035 | C32 | semidirect |
| 21. (C7⋊C9)⋊C9 | C32 | semidirect |
| 22. C9×C7⋊C9 | C32 | semidirect |
| 38. C3×C7×C9 | 3−1+2 | semidirect |
| 81. C3×C9 | #4430 | semidirect |
| 102. C7 | #10624872 | semidirect |