Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1244 conjugacy classes of subgroups; only the 518 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 518 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 | C34 |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×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. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C7×#6891 | C3 | semidirect |
| 5. C7×C9×H(3,𝔽3) | C3 | semidirect |
| 6. H(3,𝔽3)×3−1+2 | C7 | direct (N × H) |
| 11. C3×C7×3−1+2 | C32 | semidirect |
| 15. C32×C7×C9 | C32 | semidirect |
| 16. C7×C32⋊C9 | C32 | semidirect |
| 17. C7×C32⋊C9 | C32 | semidirect |
| 18. C32×3−1+2 | C3×C7 | semidirect |
| 20. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 21. #6891 | C3×C7 | semidirect |
| 22. C9×H(3,𝔽3) | C3×C7 | semidirect |
| 31. C7×3−1+2 | H(3,𝔽3) | direct (N × H) |
| 33. C7×H(3,𝔽3) | 3−1+2 | direct (N × H) |
| 41. C3×3−1+2 | C32×C7 | semidirect |
| 45. C32×C9 | C32×C7 | semidirect |
| 46. C32⋊C9 | C32×C7 | semidirect |
| 47. C32⋊C9 | C32×C7 | semidirect |
| 57. C32×C7 | C3×3−1+2 | semidirect |
| 60. C7×C9 | C3×H(3,𝔽3) | semidirect |
| 69. 3−1+2 | C7×H(3,𝔽3) | direct (N × H) |
| 71. H(3,𝔽3) | C7×3−1+2 | direct (N × H) |
| 90. C32 | C3×C7×3−1+2 | semidirect |
| 93. C9 | C3×C7×H(3,𝔽3) | semidirect |
| 94. C7 | H(3,𝔽3)×3−1+2 | direct (N × H) |