Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
662 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 265 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Fitting | C7×#6893 | C3 |
| hypercenter | #6893 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624877 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6893 | |
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. #13133570 | C3 | semidirect |
| 6. #13133560 | C3 | semidirect |
| 7. #13133560 | C3 | semidirect |
| 9. #13133540 | C3 | semidirect |
| 10. 3−1+2×C7⋊C9 | C3 | semidirect |
| 11. 3−1+2×C7⋊C9 | C3 | semidirect |
| 13. #13133527 | C3 | semidirect |
| 14. C3×C9×C7⋊C9 | C3 | semidirect |
| 197. C7 | #10624877 | semidirect |