Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1166 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 301 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 | C3×C7×#737 | C3 |
| hypercenter | C3×#737 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624869 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C3×C9 ◁ C3×#737 | |
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. #13133557 | C3 | semidirect |
| 4. #13133554 | C3 | semidirect |
| 5. #13133547 | C3 | semidirect |
| 6. #13133543 | C3 | semidirect |
| 8. C9×C7⋊H(3,𝔽3) | C3 | semidirect |
| 9. C3×C7×#737 | C3 | semidirect |
| 14. C3×C7×3−1+2 | C32 | semidirect |
| 17. C32×C7×C9 | C32 | semidirect |
| 23. C3×#4428 | C32 | semidirect |
| 24. C3×#4427 | C32 | semidirect |
| 28. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 29. C32⋊(C7⋊C9) | C32 | semidirect |
| 31. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 33. C3×#737 | ΓL(1,𝔽8) | semidirect |
| 51. C3×C7×C9 | H(3,𝔽3) | semidirect |
| 73. C3×3−1+2 | C3×ΓL(1,𝔽8) | semidirect |
| 83. C32×C9 | C3×ΓL(1,𝔽8) | semidirect |
| 97. C3×ΓL(1,𝔽8) | #737 | semidirect |
| 124. C3×C9 | C7⋊H(3,𝔽3) | semidirect |
| 150. C7 | #10624869 | semidirect |