Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
692 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 692 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 | C33 | C32×ΓL(1,𝔽8) |
| commutator | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C3×C7×C32⋊C9 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C3×C32⋊C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6898 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C3×C32⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13133582 | C3 | direct (N × H) |
| 2. C3×#10588036 | C3 | semidirect |
| 3. C3×#10588035 | C3 | semidirect |
| 4. C3×(C7⋊C9)⋊C9 | C3 | semidirect |
| 5. C3×(C7⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×(C7⋊C9)⋊C9 | C3 | semidirect |
| 9. C3×C9×C7⋊C9 | C3 | semidirect |
| 24. #10588036 | C32 | semidirect |
| 25. #10588035 | C32 | semidirect |
| 26. (C7⋊C9)⋊C9 | C32 | semidirect |
| 27. (C7⋊C9)⋊C9 | C32 | semidirect |
| 28. (C7⋊C9)⋊C9 | C32 | semidirect |
| 29. C9×C7⋊C9 | C32 | semidirect |
| 117. C3×C7 | #6898 | semidirect |
| 137. C7 | C3×#6898 | semidirect |
| 139. C3 | #13133582 | direct (N × H) |