Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
814 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 165 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×#385 | C2 |
| hypercenter | #385 | D43 |
| hypocenter | C43 | #2412 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063309 | C2 | semidirect |
| 3. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 4. C2×C22⋊C4×D43 | C2 | semidirect |
| 5. #14582826 | C2 | semidirect |
| 6. #14582816 | C2 | semidirect |
| 7. #14582778 | C2 | semidirect |
| 8. #14582777 | C2 | semidirect |
| 9. #14582760 | C2 | semidirect |
| 10. #14582756 | C2 | semidirect |
| 11. C43×#385 | C2 | semidirect |
| 20. C2×C4⋊Dic43 | C22 | semidirect |
| 28. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 29. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 31. C43⋊#95 | C22 | semidirect |
| 32. C43⋊#95 | C22 | semidirect |
| 33. C43⋊#95 | C22 | semidirect |
| 35. C2×C4⋊C4×C43 | C22 | semidirect |
| 38. #95×C43 | C22 | semidirect |
| 72. C22⋊C4×C43 | D4 | semidirect |
| 158. C2×D43 | #123 | semidirect |
| 184. #385 | D43 | semidirect |
| 187. C43 | #2412 | semidirect |
| 198. C2×C4⋊C4 | C2×D43 | semidirect |
| 214. #95 | C2×D43 | semidirect |
| 257. C22⋊C4 | D172 | semidirect |