Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1328 conjugacy classes of subgroups; only the 548 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 548 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C7 | C33 |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C7×3−1+2 | C3 | semidirect |
| 3. C33×C7×C9 | C3 | semidirect |
| 4. C7×C9⋊H(3,𝔽3) | C3 | direct (N × H) |
| 5. C3×C7×C32⋊C9 | C3 | semidirect |
| 6. C3×C7×C32⋊C9 | C3 | semidirect |
| 7. C3×C9⋊H(3,𝔽3) | C7 | direct (N × H) |
| 11. C3×C7×3−1+2 | C32 | semidirect |
| 18. C32×C7×C9 | C32 | semidirect |
| 19. C7×C32⋊C9 | C32 | semidirect |
| 20. C7×C32⋊C9 | C32 | semidirect |
| 21. C32×3−1+2 | C3×C7 | semidirect |
| 23. C33×C9 | C3×C7 | semidirect |
| 24. C9⋊H(3,𝔽3) | C3×C7 | direct (N × H) |
| 25. C3×C32⋊C9 | C3×C7 | semidirect |
| 26. C3×C32⋊C9 | C3×C7 | semidirect |
| 32. C33×C7 | 3−1+2 | semidirect |
| 41. C3×C7×C9 | H(3,𝔽3) | semidirect |
| 48. C3×3−1+2 | C32×C7 | semidirect |
| 55. C32×C9 | C32×C7 | semidirect |
| 56. C32⋊C9 | C32×C7 | semidirect |
| 57. C32⋊C9 | C32×C7 | semidirect |
| 67. C32×C7 | C3×3−1+2 | semidirect |
| 72. C7×C9 | C3×H(3,𝔽3) | semidirect |
| 78. C33 | C7×3−1+2 | semidirect |
| 87. C3×C9 | C7×H(3,𝔽3) | semidirect |
| 93. C3×C7 | C9⋊H(3,𝔽3) | direct (N × H) |
| 106. C32 | C3×C7×3−1+2 | semidirect |
| 111. C9 | C3×C7×H(3,𝔽3) | semidirect |
| 112. C7 | C3×C9⋊H(3,𝔽3) | direct (N × H) |
| 115. C3 | C7×C9⋊H(3,𝔽3) | direct (N × H) |