Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 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 | C4 | C22×D172 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C2×#131×C43 | C2 |
| socle | C2×C43 | C23×D4 |
| hypercenter | C2×#131 | D43 |
| hypocenter | C43 | #3584 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C2×#41 ◁ C2×#131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583735 | C2 | semidirect |
| 2. #14583716 | C2 | semidirect |
| 3. #14583711 | C2 | semidirect |
| 4. #14583704 | C2 | semidirect |
| 5. #14583699 | C2 | semidirect |
| 6. C2×#13063347 | C2 | semidirect |
| 7. C2×#131×C43 | C2 | semidirect |
| 9. #13063372 | C22 | semidirect |
| 10. #13063371 | C22 | semidirect |
| 12. C2×#10621898 | C22 | semidirect |
| 14. #13063358 | C22 | semidirect |
| 15. #13063353 | C22 | semidirect |
| 16. #13063347 | C22 | semidirect |
| 17. #13063347 | C22 | semidirect |
| 18. #13063347 | C22 | semidirect |
| 19. #13063347 | C22 | semidirect |
| 20. C2×Dic172 | C22 | semidirect |
| 21. C2×#10621873 | C22 | semidirect |
| 22. C2×D344 | C22 | semidirect |
| 24. #131×C43 | C22 | semidirect |
| 25. #131×C43 | C22 | semidirect |
| 26. C2×M16×C43 | C22 | semidirect |
| 27. C22×C8×C43 | C22 | semidirect |
| 96. C2×#131 | D43 | semidirect |
| 97. C43 | #3584 | semidirect |
| 114. #131 | C2×D43 | semidirect |
| 115. #131 | C2×D43 | semidirect |
| 116. C2×M16 | C2×D43 | semidirect |
| 117. C22×C8 | C2×D43 | semidirect |