Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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×#6894 | C3 |
| hypercenter | #6894 | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624879 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6894 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13133597 | C3 | semidirect |
| 3. #13133589 | C3 | semidirect |
| 4. #13133576 | C3 | semidirect |
| 5. #13133574 | C3 | semidirect |
| 6. #13133565 | C3 | semidirect |
| 7. #13133564 | C3 | semidirect |
| 8. #13133560 | C3 | semidirect |
| 11. #4427⋊C9 | C3 | semidirect |
| 12. #4427⋊C9 | C3 | semidirect |
| 13. #13133527 | C3 | semidirect |
| 14. C3×C9×C7⋊C9 | C3 | semidirect |
| 15. C7×#6894 | C3 | semidirect |
| 62. #6894 | ΓL(1,𝔽8) | semidirect |
| 80. C3×C7⋊C9 | 3−1+2 | semidirect |
| 142. C7×C9 | #737 | semidirect |
| 151. C7⋊C9 | #737 | semidirect |
| 202. C9 | #10588065 | semidirect |
| 203. C7 | #10624879 | semidirect |