Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
884 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 313 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×#6896 | C3 |
| hypercenter | #6896 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6896 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6896 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133576 | C3 | semidirect |
| 3. #13133575 | C3 | semidirect |
| 4. #13133574 | C3 | semidirect |
| 5. #13133573 | C3 | semidirect |
| 6. #13133572 | C3 | semidirect |
| 7. #13133571 | C3 | semidirect |
| 8. ΓL(1,𝔽8)×C9⋊C9 | C3 | semidirect |
| 9. ΓL(1,𝔽8)×C9⋊C9 | C3 | semidirect |
| 11. C92×ΓL(1,𝔽8) | C3 | semidirect |
| 12. C7×#6896 | C3 | semidirect |
| 26. C7×C9⋊C9 | C32 | semidirect |
| 27. C7×C9⋊C9 | C32 | semidirect |
| 29. C7×C92 | C32 | semidirect |
| 33. #10588036 | C32 | semidirect |
| 34. #10588036 | C32 | semidirect |
| 35. #10588035 | C32 | semidirect |
| 36. #10588035 | C32 | semidirect |
| 37. (C7⋊C9)⋊C9 | C32 | semidirect |
| 38. (C7⋊C9)⋊C9 | C32 | semidirect |
| 39. (C7⋊C9)⋊C9 | C32 | semidirect |
| 40. (C7⋊C9)⋊C9 | C32 | semidirect |
| 41. (C7⋊C9)⋊C9 | C32 | semidirect |
| 42. (C7⋊C9)⋊C9 | C32 | semidirect |
| 43. C9×C7⋊C9 | C32 | semidirect |
| 44. C9×C7⋊C9 | C32 | semidirect |
| 52. #6896 | ΓL(1,𝔽8) | direct (N × H) |
| 80. C9×ΓL(1,𝔽8) | 3−1+2 | semidirect |
| 103. C9⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 104. C9⋊C9 | C3×ΓL(1,𝔽8) | semidirect |
| 111. C92 | C3×ΓL(1,𝔽8) | semidirect |
| 124. C7×C9 | C3×3−1+2 | semidirect |
| 129. C7⋊C9 | C3×3−1+2 | semidirect |
| 158. ΓL(1,𝔽8) | #6896 | direct (N × H) |
| 176. C9 | ΓL(1,𝔽8)×3−1+2 | semidirect |
| 177. C7 | C3×#6896 | semidirect |