Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
2672 conjugacy classes of subgroups; only the 512 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 512 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 | H(3,𝔽3) |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C7 ◁ C34×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C35×C7 | C3 | semidirect |
| 2. C32×C7×3−1+2 | C3 | semidirect |
| 3. C32×C7×H(3,𝔽3) | C3 | semidirect |
| 4. C3×C7×AΣL(1,𝔽27) | C3 | direct (N × H) |
| 5. C32×AΣL(1,𝔽27) | C7 | direct (N × H) |
| 11. C34×C7 | C32 | semidirect |
| 13. C3×C7×3−1+2 | C32 | semidirect |
| 15. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 17. C7×AΣL(1,𝔽27) | C32 | direct (N × H) |
| 18. C35 | C3×C7 | semidirect |
| 19. C32×3−1+2 | C3×C7 | semidirect |
| 20. C32×H(3,𝔽3) | C3×C7 | semidirect |
| 21. C3×AΣL(1,𝔽27) | C3×C7 | direct (N × H) |
| 33. C33×C7 | C33 | semidirect |
| 35. C7×3−1+2 | C33 | semidirect |
| 37. C7×H(3,𝔽3) | C33 | semidirect |
| 44. C34 | C32×C7 | semidirect |
| 46. C3×3−1+2 | C32×C7 | semidirect |
| 48. C3×H(3,𝔽3) | C32×C7 | semidirect |
| 50. AΣL(1,𝔽27) | C32×C7 | direct (N × H) |
| 59. C32×C7 | AΣL(1,𝔽27) | direct (N × H) |
| 75. C33 | C33×C7 | semidirect |
| 77. 3−1+2 | C33×C7 | semidirect |
| 79. H(3,𝔽3) | C33×C7 | semidirect |
| 85. C3×C7 | C3×AΣL(1,𝔽27) | direct (N × H) |
| 95. C32 | C7×AΣL(1,𝔽27) | direct (N × H) |
| 100. C7 | C32×AΣL(1,𝔽27) | direct (N × H) |
| 105. C3 | C3×C7×AΣL(1,𝔽27) | direct (N × H) |