Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
950 conjugacy classes of subgroups; only the 482 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 482 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C7 | C34 |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 3. C7×#6891 | C3 | semidirect |
| 4. C7×C9×H(3,𝔽3) | C3 | semidirect |
| 5. C3×C7×C32⋊C9 | C3 | semidirect |
| 6. #10624897 | C7 | direct (N × H) |
| 8. C3×C7×3−1+2 | C32 | semidirect |
| 12. C32×C7×C9 | C32 | semidirect |
| 15. C7×C32⋊C9 | C32 | semidirect |
| 16. C7×C32⋊C9 | C32 | semidirect |
| 17. C7×C32⋊C9 | C32 | semidirect |
| 19. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 20. #6891 | C3×C7 | semidirect |
| 21. C9×H(3,𝔽3) | C3×C7 | semidirect |
| 22. C3×C32⋊C9 | C3×C7 | semidirect |
| 32. C7×H(3,𝔽3) | 3−1+2 | semidirect |
| 37. C3×3−1+2 | C32×C7 | semidirect |
| 41. C32×C9 | C32×C7 | semidirect |
| 44. C32⋊C9 | C32×C7 | semidirect |
| 45. C32⋊C9 | C32×C7 | semidirect |
| 46. C32⋊C9 | C32×C7 | semidirect |
| 72. H(3,𝔽3) | C7×3−1+2 | semidirect |
| 99. C7 | #10624897 | direct (N × H) |