Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1166 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 292 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×#6891 | C3 |
| hypercenter | #6891 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624869 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6891 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#10588065 | C3 | semidirect |
| 2. C33×C7⋊C9 | C3 | semidirect |
| 3. #13133557 | C3 | semidirect |
| 4. #13133553 | C3 | semidirect |
| 5. #13133552 | C3 | semidirect |
| 6. #13133546 | C3 | semidirect |
| 8. #13133531 | C3 | semidirect |
| 9. C7×#6891 | C3 | semidirect |
| 23. C3×#4428 | C32 | semidirect |
| 24. C3×#4427 | C32 | semidirect |
| 25. C3×C9×ΓL(1,𝔽8) | C32 | semidirect |
| 28. (C3×ΓL(1,𝔽8))⋊C9 | C32 | semidirect |
| 35. #6891 | ΓL(1,𝔽8) | semidirect |
| 52. C3×C7⋊C9 | H(3,𝔽3) | semidirect |
| 84. C32×C7 | #737 | semidirect |
| 129. C32 | #10588065 | semidirect |
| 137. C7 | #10624869 | semidirect |