Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1196 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 476 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 | C3×H(3,𝔽3) |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C7 ◁ C34×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 |
| 2. C32×C7×H(3,𝔽3) | C3 | semidirect |
| 3. C32×C7×H(3,𝔽3) | C3 | semidirect |
| 4. C7×#6909 | C3 | direct (N × H) |
| 5. C3×C7×AΣL(1,𝔽27) | C3 | semidirect |
| 6. C3×#6909 | C7 | direct (N × H) |
| 9. C34×C7 | C32 | semidirect |
| 13. C3×C7×3−1+2 | C32 | semidirect |
| 14. C3×C7×3−1+2 | C32 | semidirect |
| 21. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 22. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 24. C7×AΣL(1,𝔽27) | C32 | semidirect |
| 25. C32×3−1+2 | C3×C7 | semidirect |
| 26. C32×H(3,𝔽3) | C3×C7 | semidirect |
| 27. C32×H(3,𝔽3) | C3×C7 | semidirect |
| 28. #6909 | C3×C7 | direct (N × H) |
| 29. C3×AΣL(1,𝔽27) | C3×C7 | semidirect |
| 42. C33×C7 | C33 | semidirect |
| 46. C7×3−1+2 | C33 | semidirect |
| 56. C34 | C32×C7 | semidirect |
| 60. C3×3−1+2 | C32×C7 | semidirect |
| 61. C3×3−1+2 | C32×C7 | semidirect |
| 68. C3×H(3,𝔽3) | C32×C7 | semidirect |
| 69. C3×H(3,𝔽3) | C32×C7 | semidirect |
| 71. AΣL(1,𝔽27) | C32×C7 | semidirect |
| 102. C33 | C33×C7 | semidirect |
| 106. 3−1+2 | C33×C7 | semidirect |
| 120. C3×C7 | #6909 | direct (N × H) |
| 140. C7 | C3×#6909 | direct (N × H) |
| 147. C3 | C7×#6909 | direct (N × H) |