Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#339 | C2 |
| socle | C22×C43 | C4×D4 |
| hypercenter | #339 | D43 |
| hypocenter | C43 | #1764 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #339 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14582855 | C2 | semidirect |
| 5. C2×C4×C43⋊C8 | C2 | semidirect |
| 6. #14582663 | C2 | semidirect |
| 7. C43×#339 | C2 | semidirect |
| 10. #13063333 | C4 | semidirect |
| 16. #13063253 | C4 | semidirect |
| 17. #13063248 | C4 | semidirect |
| 18. #13063245 | C4 | semidirect |
| 105. #339 | D43 | semidirect |
| 106. C43 | #1764 | semidirect |