Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 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, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#380 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #380 | D43 |
| hypocenter | C43 | D4×C22⋊C4 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063287 | C2 | semidirect |
| 3. C2×C22⋊C4×D43 | C2 | semidirect |
| 4. #14582800 | C2 | semidirect |
| 5. #14582777 | C2 | semidirect |
| 6. #14582754 | C2 | semidirect |
| 7. C4×C22⋊Dic43 | C2 | semidirect |
| 8. C43×#380 | C2 | semidirect |
| 11. C22×D172 | C4 | semidirect |
| 15. C22×C4×D43 | C22 | semidirect |
| 19. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 23. C2×C4×Dic43 | C22 | semidirect |
| 24. C43⋊#95 | C22 | semidirect |
| 26. C2×C4⋊C4×C43 | C22 | semidirect |
| 28. #95×C43 | C22 | semidirect |
| 34. C23×D43 | C2×C4 | semidirect |
| 38. C22×C4×C43 | C2×C4 | semidirect |
| 48. C2×D172 | C2×C4 | semidirect |
| 49. C2×D172 | C2×C4 | semidirect |
| 57. C22⋊Dic43 | D4 | semidirect |
| 96. C2×Dic43 | C2×D4 | semidirect |
| 99. D172 | C22⋊C4 | semidirect |
| 105. C22×C43 | C4×D4 | semidirect |
| 121. C2×D43 | C2×C22⋊C4 | semidirect |
| 124. C4×C43 | C2×C22⋊C4 | semidirect |
| 141. #380 | D43 | semidirect |
| 144. C43 | D4×C22⋊C4 | semidirect |
| 154. C2×C4⋊C4 | C2×D43 | semidirect |
| 164. #95 | C2×D43 | semidirect |
| 186. C22×C4 | C4×D43 | semidirect |
| 252. C22 | #13063287 | semidirect |
| 262. C4 | C22⋊C4×D43 | semidirect |