Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator | C2×C43 | C24×C4 |
| Fitting | C43×#519 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | #519 | D43 |
| hypocenter | C43 | #3428 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583381 | C2 | semidirect |
| 3. #14583377 | C2 | semidirect |
| 4. #14583373 | C2 | semidirect |
| 5. C4×#10621902 | C2 | semidirect |
| 6. #117×D43 | C2 | semidirect |
| 7. C43×#519 | C2 | semidirect |
| 8. C2×#10621902 | C4 | semidirect |
| 13. Q8×Dic43 | C22 | semidirect |
| 14. C4×D172 | C22 | semidirect |
| 15. #13063287 | C22 | semidirect |
| 17. #13063283 | C22 | semidirect |
| 18. #13063282 | C22 | semidirect |
| 20. C4⋊C4×D43 | C22 | semidirect |
| 22. C42×D43 | C22 | semidirect |
| 24. C4×Q8×C43 | C22 | semidirect |
| 27. C2×Q8×C43 | C2×C4 | semidirect |
| 31. #10621902 | C2×C4 | semidirect |
| 32. #10621902 | C2×C4 | semidirect |
| 33. C2×D172 | C2×C4 | semidirect |
| 35. C2×C4×D43 | C2×C4 | semidirect |
| 83. #519 | D43 | semidirect |
| 87. C43 | #3428 | semidirect |
| 95. C4×Q8 | C2×D43 | semidirect |
| 109. C2×Q8 | C4×D43 | semidirect |