Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
788 conjugacy classes of subgroups; only the 446 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 446 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. C7×#6893 | C3 | semidirect |
| 2. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 3. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C7×#6891 | C3 | semidirect |
| 6. C7×C9×H(3,𝔽3) | C3 | semidirect |
| 7. C3×C7×C32⋊C9 | C3 | semidirect |
| 8. #10624905 | C7 | direct (N × H) |
| 11. C3×C7×3−1+2 | C32 | semidirect |
| 16. C32×C7×C9 | C32 | semidirect |
| 23. C7×C32⋊C9 | C32 | semidirect |
| 24. C7×C32⋊C9 | C32 | semidirect |
| 25. #6893 | C3×C7 | semidirect |
| 26. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 27. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 28. #6891 | C3×C7 | semidirect |
| 30. C9×H(3,𝔽3) | C3×C7 | semidirect |
| 31. C3×C32⋊C9 | C3×C7 | semidirect |
| 51. C3×3−1+2 | C32×C7 | semidirect |
| 56. C32×C9 | C32×C7 | semidirect |
| 63. C32⋊C9 | C32×C7 | semidirect |
| 64. C32⋊C9 | C32×C7 | semidirect |
| 125. C7 | #10624905 | direct (N × H) |