Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
948 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C7 | C32×H(3,𝔽3) |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C7 ◁ C3×C7×3−1+2 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×3−1+4 | C3 | semidirect |
| 2. C3×C7×#737 | C3 | semidirect |
| 3. C7×#6913 | C3 | semidirect |
| 4. C7×#6912 | C3 | semidirect |
| 5. C7×#6911 | C3 | semidirect |
| 6. C7×#6909 | C3 | semidirect |
| 7. C7×#6908 | C3 | semidirect |
| 8. C3×C7×#731 | C3 | semidirect |
| 9. #10624935 | C7 | direct (N × H) |
| 12. C7×#737 | C32 | semidirect |
| 17. C3×C7×3−1+2 | C32 | semidirect |
| 21. C32×C7×C9 | C32 | semidirect |
| 22. C7×#733 | C32 | semidirect |
| 24. C7×#731 | C32 | semidirect |
| 25. C7×#731 | C32 | semidirect |
| 26. C7×AΣL(1,𝔽27) | C32 | semidirect |
| 27. 3−1+4 | C3×C7 | semidirect |
| 28. C3×#737 | C3×C7 | semidirect |
| 29. #6913 | C3×C7 | semidirect |
| 30. #6912 | C3×C7 | semidirect |
| 31. #6911 | C3×C7 | semidirect |
| 32. #6909 | C3×C7 | semidirect |
| 33. #6908 | C3×C7 | semidirect |
| 34. C3×#731 | C3×C7 | semidirect |
| 58. #737 | C32×C7 | semidirect |
| 63. C3×3−1+2 | C32×C7 | semidirect |
| 67. C32×C9 | C32×C7 | semidirect |
| 68. #733 | C32×C7 | semidirect |
| 70. #731 | C32×C7 | semidirect |
| 71. #731 | C32×C7 | semidirect |
| 72. AΣL(1,𝔽27) | C32×C7 | semidirect |
| 123. C7 | #10624935 | direct (N × H) |