Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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, socle | C23×C43 | C24 |
| Fitting | C43×#390 | C2 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2679 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063295 | C2 | semidirect |
| 2. C2×#13063293 | C2 | semidirect |
| 3. #14582816 | C2 | semidirect |
| 4. #14582815 | C2 | semidirect |
| 5. #14582801 | C2 | semidirect |
| 6. C43×#390 | C2 | semidirect |
| 7. C24×D43 | C22 | semidirect |
| 13. C2×C4⋊Dic43 | C22 | semidirect |
| 14. C2×C22⋊Dic43 | C22 | semidirect |
| 15. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 16. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 17. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 18. C43⋊#95 | C22 | semidirect |
| 20. C2×C4⋊C4×C43 | C22 | semidirect |
| 21. C2×C22⋊C4×C43 | C22 | semidirect |
| 22. C2×C42×C43 | C22 | semidirect |
| 32. C2×D4×C43 | D4 | semidirect |
| 44. C2×D172 | D4 | semidirect |
| 121. #390 | D43 | semidirect |
| 122. C43 | #2679 | semidirect |
| 131. C2×C4⋊C4 | C2×D43 | semidirect |
| 136. C2×C22⋊C4 | C2×D43 | semidirect |
| 137. C2×C42 | C2×D43 | semidirect |
| 156. C2×D4 | D172 | semidirect |