Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1304 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 1304 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 ◁ C34×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 |
| 2. C32×C7×H(3,𝔽3) | C3 | semidirect |
| 3. C7×#6911 | C3 | direct (N × H) |
| 4. C3×C7×#732 | C3 | semidirect |
| 5. C3×#6911 | C7 | direct (N × H) |
| 10. C3×C7×3−1+2 | C32 | semidirect |
| 13. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 14. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 15. C32×C7×C9 | C32 | semidirect |
| 16. C7×#732 | C32 | semidirect |
| 17. C32×3−1+2 | C3×C7 | semidirect |
| 18. C32×H(3,𝔽3) | C3×C7 | semidirect |
| 19. #6911 | C3×C7 | direct (N × H) |
| 20. C3×#732 | C3×C7 | semidirect |
| 32. C7×H(3,𝔽3) | C33 | semidirect |
| 35. C3×C7×C9 | C33 | semidirect |
| 40. C3×3−1+2 | C32×C7 | semidirect |
| 43. C3×H(3,𝔽3) | C32×C7 | semidirect |
| 44. C3×H(3,𝔽3) | C32×C7 | semidirect |
| 45. C32×C9 | C32×C7 | semidirect |
| 46. #732 | C32×C7 | semidirect |
| 70. H(3,𝔽3) | C33×C7 | semidirect |
| 73. C3×C9 | C33×C7 | semidirect |
| 78. C3×C7 | #6911 | direct (N × H) |
| 92. C7 | C3×#6911 | direct (N × H) |
| 97. C3 | C7×#6911 | direct (N × H) |