Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#520 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #520 | D43 |
| hypocenter | C43 | #2897 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #520 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063332 | C2 | semidirect |
| 3. #14582903 | C2 | semidirect |
| 4. #14582898 | C2 | semidirect |
| 5. #14582893 | C2 | semidirect |
| 6. C2×#13063245 | C2 | semidirect |
| 7. C43×#520 | C2 | semidirect |
| 9. #13063371 | C4 | semidirect |
| 15. C2×#10621877 | C22 | semidirect |
| 16. C22×C43⋊C8 | C22 | semidirect |
| 17. #13063248 | C22 | semidirect |
| 18. #13063248 | C22 | semidirect |
| 19. #13063245 | C22 | semidirect |
| 20. #13063245 | C22 | semidirect |
| 21. #13063245 | C22 | semidirect |
| 25. #117×C43 | C22 | semidirect |
| 26. C2×C4⋊C4×C43 | C22 | semidirect |
| 38. #10621898 | C2×C4 | semidirect |
| 41. C2×D172 | C2×C4 | semidirect |
| 100. #520 | D43 | semidirect |
| 105. C43 | #2897 | semidirect |
| 118. #117 | C2×D43 | semidirect |
| 119. C2×C4⋊C4 | C2×D43 | semidirect |