Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
662 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 268 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 | C7×C9×H(3,𝔽3) | C3 |
| hypercenter | C9×H(3,𝔽3) | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624877 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C3×C9 ◁ C9×H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13133585 | C3 | semidirect |
| 2. #13133582 | C3 | semidirect |
| 3. #13133577 | C3 | semidirect |
| 4. #13133571 | C3 | semidirect |
| 5. #13133568 | C3 | semidirect |
| 6. #13133567 | C3 | semidirect |
| 7. #13133566 | C3 | semidirect |
| 8. #13133565 | C3 | semidirect |
| 11. C9×#4430 | C3 | semidirect |
| 12. C9×#4430 | C3 | semidirect |
| 13. #13133530 | C3 | semidirect |
| 14. C3×C9×C7⋊C9 | C3 | semidirect |
| 193. C7 | #10624877 | semidirect |