Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
1718 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1718 conjugacy classes of subgroups — too many to draw. Only its 274 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×C32⋊H(3,𝔽3) | C3 |
| hypercenter | C32⋊H(3,𝔽3) | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624880 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C32⋊H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C7⋊H(3,𝔽3) | C3 | semidirect |
| 2. C3×ΓL(1,𝔽8)×H(3,𝔽3) | C3 | semidirect |
| 3. #13133542 | C3 | semidirect |
| 4. (C3×ΓL(1,𝔽8))⋊H(3,𝔽3) | C3 | semidirect |
| 5. (C3×ΓL(1,𝔽8))⋊H(3,𝔽3) | C3 | semidirect |
| 6. C7×C32⋊H(3,𝔽3) | C3 | semidirect |
| 8. C34×C7 | C32 | semidirect |
| 10. C33×ΓL(1,𝔽8) | C32 | semidirect |
| 11. C33×ΓL(1,𝔽8) | C32 | semidirect |
| 12. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 13. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 15. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 16. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 17. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 18. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 19. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 26. C32⋊H(3,𝔽3) | ΓL(1,𝔽8) | semidirect |
| 37. C32×ΓL(1,𝔽8) | H(3,𝔽3) | semidirect |
| 51. C34 | C3×ΓL(1,𝔽8) | semidirect |
| 59. C3×H(3,𝔽3) | C3×ΓL(1,𝔽8) | semidirect |
| 60. C3×H(3,𝔽3) | C3×ΓL(1,𝔽8) | semidirect |
| 126. C7 | #10624880 | semidirect |