Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D43 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C43×#585 | C2 |
| socle | C2×C43 | C23×D4 |
| hypercenter | #585 | D43 |
| hypocenter | C43 | #3586 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063372 | C2 | semidirect |
| 2. #14583714 | C2 | semidirect |
| 3. #14583710 | C2 | semidirect |
| 4. #14583697 | C2 | semidirect |
| 5. C2×#13063355 | C2 | semidirect |
| 6. #14583666 | C2 | semidirect |
| 7. C43×#585 | C2 | semidirect |
| 9. #13063372 | C22 | semidirect |
| 10. C2×#10621898 | C22 | semidirect |
| 12. C22×Dic86 | C22 | semidirect |
| 14. #13063356 | C22 | semidirect |
| 15. #13063355 | C22 | semidirect |
| 16. #13063355 | C22 | semidirect |
| 17. #13063351 | C22 | semidirect |
| 18. #13063350 | C22 | semidirect |
| 19. #13063345 | C22 | semidirect |
| 20. C2×#10621885 | C22 | semidirect |
| 21. C2×#10621883 | C22 | semidirect |
| 22. #13063332 | C22 | semidirect |
| 23. C2×#10621877 | C22 | semidirect |
| 25. 2−1+4×C43 | C22 | semidirect |
| 27. H(5,𝔽2)×C43 | C22 | semidirect |
| 113. #585 | D43 | semidirect |
| 120. C43 | #3586 | semidirect |
| 124. 2−1+4 | C2×D43 | semidirect |
| 126. H(5,𝔽2) | C2×D43 | semidirect |