Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
992 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 992 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 ◁ C32×C7×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C7×#737 | C3 | semidirect |
| 2. C32×C7×3−1+2 | C3 | semidirect |
| 3. C7×#6913 | C3 | direct (N × H) |
| 4. C3×C7×#733 | C3 | semidirect |
| 5. C3×C7×#732 | C3 | semidirect |
| 6. C3×C7×#731 | C3 | semidirect |
| 7. C3×C7×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×#6913 | C7 | direct (N × H) |
| 11. C7×#737 | C32 | semidirect |
| 16. C3×C7×3−1+2 | C32 | semidirect |
| 22. C7×#733 | C32 | semidirect |
| 23. C7×#732 | C32 | semidirect |
| 24. C7×#731 | C32 | semidirect |
| 25. C7×AΣL(1,𝔽27) | C32 | semidirect |
| 26. C3×#737 | C3×C7 | semidirect |
| 27. C32×3−1+2 | C3×C7 | semidirect |
| 28. #6913 | C3×C7 | direct (N × H) |
| 29. C3×#733 | C3×C7 | semidirect |
| 30. C3×#732 | C3×C7 | semidirect |
| 31. C3×#731 | C3×C7 | semidirect |
| 32. C3×AΣL(1,𝔽27) | C3×C7 | semidirect |
| 58. #737 | C32×C7 | semidirect |
| 63. C3×3−1+2 | C32×C7 | semidirect |
| 69. #733 | C32×C7 | semidirect |
| 70. #732 | C32×C7 | semidirect |
| 71. #731 | C32×C7 | semidirect |
| 72. AΣL(1,𝔽27) | C32×C7 | semidirect |
| 114. C3×C7 | #6913 | direct (N × H) |
| 130. C7 | C3×#6913 | direct (N × H) |
| 135. C3 | C7×#6913 | direct (N × H) |