Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1166 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Fitting | C7×#6893 | C3 |
| hypercenter | #6893 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624869 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6893 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#10588065 | C3 | semidirect |
| 2. C3×#10588062 | C3 | semidirect |
| 3. C32×C9×ΓL(1,𝔽8) | C3 | semidirect |
| 4. #13133557 | C3 | semidirect |
| 5. #13133556 | C3 | semidirect |
| 6. #13133554 | C3 | semidirect |
| 7. #13133549 | C3 | semidirect |
| 8. #13133543 | C3 | semidirect |
| 10. #13133531 | C3 | semidirect |
| 11. C7×#6893 | C3 | semidirect |
| 21. C3×#4430 | C32 | semidirect |
| 24. C32×C7⋊C9 | C32 | semidirect |
| 27. C3×#4428 | C32 | semidirect |
| 28. C3×#4427 | C32 | semidirect |
| 32. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 33. C7×C32⋊C9 | C32 | semidirect |
| 34. C32⋊(C7⋊C9) | C32 | semidirect |
| 36. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 37. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 44. #6893 | ΓL(1,𝔽8) | semidirect |
| 67. C3×C7⋊C9 | H(3,𝔽3) | semidirect |
| 102. C32⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 113. C3×ΓL(1,𝔽8) | #737 | semidirect |
| 174. C7 | #10624869 | semidirect |