Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1166 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C32×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C7×C9×H(3,𝔽3) | C3 |
| hypercenter | C9×H(3,𝔽3) | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624869 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C3×C9 ◁ C9×H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#10588061 | C3 | semidirect |
| 2. C32×C9×ΓL(1,𝔽8) | C3 | semidirect |
| 3. #13133555 | C3 | semidirect |
| 4. #13133553 | C3 | semidirect |
| 5. #13133552 | C3 | semidirect |
| 6. #13133549 | C3 | semidirect |
| 7. #13133548 | C3 | semidirect |
| 8. #13133545 | C3 | semidirect |
| 9. #13133544 | C3 | semidirect |
| 11. C9×C7⋊H(3,𝔽3) | C3 | semidirect |
| 12. C9×C7⋊H(3,𝔽3) | C3 | semidirect |
| 13. C7×C9×H(3,𝔽3) | C3 | semidirect |
| 18. C32×C7×C9 | C32 | semidirect |
| 22. C3×#4430 | C32 | semidirect |
| 26. C3×#4428 | C32 | semidirect |
| 28. C3×#4427 | C32 | semidirect |
| 34. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 37. C7×C32⋊C9 | C32 | semidirect |
| 40. C32⋊(C7⋊C9) | C32 | semidirect |
| 43. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 44. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 45. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 58. C9×H(3,𝔽3) | ΓL(1,𝔽8) | semidirect |
| 91. C9×ΓL(1,𝔽8) | H(3,𝔽3) | semidirect |
| 111. C32×C9 | C3×ΓL(1,𝔽8) | semidirect |
| 122. C32⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 128. C32×C7 | #737 | semidirect |
| 140. C3×ΓL(1,𝔽8) | #737 | semidirect |
| 206. C32 | #10588061 | semidirect |
| 216. C7 | #10624869 | semidirect |