Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1082 conjugacy classes of subgroups; only the 482 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 482 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. C3×C7×#737 | C3 | semidirect |
| 2. C32×C7×3−1+2 | C3 | semidirect |
| 3. C7×#6893 | C3 | semidirect |
| 4. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 5. C7×C9⋊H(3,𝔽3) | C3 | semidirect |
| 6. C7×#6891 | C3 | semidirect |
| 8. C7×C9×H(3,𝔽3) | C3 | semidirect |
| 9. C3×C7×C32⋊C9 | C3 | semidirect |
| 10. #10624896 | C7 | direct (N × H) |
| 18. C3×C7×3−1+2 | C32 | semidirect |
| 24. C32×C7×C9 | C32 | semidirect |
| 30. C7×C32⋊C9 | C32 | semidirect |
| 31. C7×C32⋊C9 | C32 | semidirect |
| 32. C3×#737 | C3×C7 | semidirect |
| 33. C32×3−1+2 | C3×C7 | semidirect |
| 34. #6893 | C3×C7 | semidirect |
| 35. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 36. C9⋊H(3,𝔽3) | C3×C7 | semidirect |
| 37. #6891 | C3×C7 | semidirect |
| 39. C9×H(3,𝔽3) | C3×C7 | semidirect |
| 40. C3×C32⋊C9 | C3×C7 | semidirect |
| 52. C7×3−1+2 | H(3,𝔽3) | semidirect |
| 71. C3×3−1+2 | C32×C7 | semidirect |
| 77. C32×C9 | C32×C7 | semidirect |
| 83. C32⋊C9 | C32×C7 | semidirect |
| 84. C32⋊C9 | C32×C7 | semidirect |
| 98. C32×C7 | #737 | semidirect |
| 116. 3−1+2 | C7×H(3,𝔽3) | semidirect |
| 148. C32 | C7×#737 | semidirect |
| 155. C7 | #10624896 | direct (N × H) |