Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
824 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 824 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 | #10624872 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6891 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133568 | C3 | semidirect |
| 3. #13133567 | C3 | semidirect |
| 4. #13133566 | C3 | semidirect |
| 5. #13133565 | C3 | semidirect |
| 6. #13133560 | C3 | semidirect |
| 8. #13133540 | C3 | semidirect |
| 9. 3−1+2×C7⋊C9 | C3 | semidirect |
| 10. #13133527 | C3 | semidirect |
| 30. #10588036 | C32 | semidirect |
| 31. #10588035 | C32 | semidirect |
| 32. (C7⋊C9)⋊C9 | C32 | semidirect |
| 33. (C7⋊C9)⋊C9 | C32 | semidirect |
| 34. (C7⋊C9)⋊C9 | C32 | semidirect |
| 35. C9×C7⋊C9 | C32 | semidirect |
| 63. C3×C7⋊C9 | 3−1+2 | semidirect |
| 164. C7 | #10624872 | semidirect |