Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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×C9⋊H(3,𝔽3) | C3 |
| hypercenter | C9⋊H(3,𝔽3) | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624879 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C9⋊H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133593 | C3 | semidirect |
| 3. #13133585 | C3 | semidirect |
| 4. #13133572 | C3 | semidirect |
| 5. #13133571 | C3 | semidirect |
| 6. #13133566 | C3 | semidirect |
| 7. #13133565 | C3 | semidirect |
| 8. #13133564 | C3 | semidirect |
| 9. #13133563 | C3 | semidirect |
| 11. #13133540 | C3 | semidirect |
| 12. 3−1+2×C7⋊C9 | C3 | semidirect |
| 13. #13133527 | C3 | semidirect |
| 14. C3×C9×C7⋊C9 | C3 | semidirect |
| 84. C3×C7⋊C9 | 3−1+2 | semidirect |
| 141. C7×C9 | #737 | semidirect |
| 151. C7⋊C9 | #737 | semidirect |
| 202. C9 | #10588062 | semidirect |
| 203. C7 | #10624879 | semidirect |