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×D172 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C43×#568 | C2 |
| socle | C2×C43 | C23×D4 |
| hypercenter | #568 | D43 |
| hypocenter | C43 | #3586 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583735 | C2 | semidirect |
| 2. C2×#13063372 | C2 | semidirect |
| 3. #14583716 | C2 | semidirect |
| 4. #14583711 | C2 | semidirect |
| 5. #14583699 | C2 | semidirect |
| 6. C2×#13063358 | C2 | semidirect |
| 7. C43×#568 | C2 | semidirect |
| 10. #13063372 | C22 | semidirect |
| 11. #13063372 | C22 | semidirect |
| 12. #13063371 | C22 | semidirect |
| 15. C2×#10621898 | C22 | semidirect |
| 18. C22×Dic86 | C22 | semidirect |
| 20. #13063358 | C22 | semidirect |
| 21. #13063358 | C22 | semidirect |
| 22. #13063358 | C22 | semidirect |
| 23. #13063353 | C22 | semidirect |
| 24. #13063353 | C22 | semidirect |
| 25. #13063347 | C22 | semidirect |
| 26. C2×Dic172 | C22 | semidirect |
| 27. C2×#10621873 | C22 | semidirect |
| 29. #131×C43 | C22 | semidirect |
| 30. C2×M16×C43 | C22 | semidirect |
| 119. #568 | D43 | semidirect |
| 120. C43 | #3586 | semidirect |
| 142. #131 | C2×D43 | semidirect |
| 143. C2×M16 | C2×D43 | semidirect |