Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
788 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 788 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×#6899 | C3 |
| hypercenter | #6899 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6899 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6899 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133592 | C3 | semidirect |
| 3. #13133591 | C3 | semidirect |
| 4. #13133590 | C3 | semidirect |
| 5. #13133589 | C3 | semidirect |
| 6. #13133588 | C3 | semidirect |
| 7. #13133587 | C3 | semidirect |
| 8. #13133586 | C3 | semidirect |
| 9. #13133585 | C3 | semidirect |
| 10. ΓL(1,𝔽8)×C9⋊C9 | C3 | semidirect |
| 11. ΓL(1,𝔽8)×C9⋊C9 | C3 | semidirect |
| 13. C92×ΓL(1,𝔽8) | C3 | semidirect |
| 14. C7×#6899 | C3 | semidirect |
| 28. C7×C9⋊C9 | C32 | semidirect |
| 29. C7×C9⋊C9 | C32 | semidirect |
| 31. C7×C92 | C32 | semidirect |
| 37. #10588036 | C32 | semidirect |
| 38. #10588036 | C32 | semidirect |
| 39. #10588035 | C32 | semidirect |
| 40. #10588035 | C32 | semidirect |
| 41. (C7⋊C9)⋊C9 | C32 | semidirect |
| 42. (C7⋊C9)⋊C9 | C32 | semidirect |
| 43. (C7⋊C9)⋊C9 | C32 | semidirect |
| 44. (C7⋊C9)⋊C9 | C32 | semidirect |
| 45. (C7⋊C9)⋊C9 | C32 | semidirect |
| 46. (C7⋊C9)⋊C9 | C32 | semidirect |
| 47. C9×C7⋊C9 | C32 | semidirect |
| 48. C9×C7⋊C9 | C32 | semidirect |
| 58. #6899 | ΓL(1,𝔽8) | direct (N × H) |
| 111. C9⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 112. C9⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 121. C92 | C3×ΓL(1,𝔽8) | semidirect |
| 173. ΓL(1,𝔽8) | #6899 | direct (N × H) |
| 194. C7 | C3×#6899 | semidirect |