Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×#384 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #384 | D43 |
| hypocenter | C43 | #2317 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14582794 | C2 | semidirect |
| 6. #14582768 | C2 | semidirect |
| 7. #14582765 | C2 | semidirect |
| 8. #14582764 | C2 | semidirect |
| 9. C43×#384 | C2 | semidirect |
| 13. #13063282 | C4 | semidirect |
| 47. C42×C43 | C2×C4 | semidirect |
| 54. Dic43⋊C4 | C2×C4 | semidirect |
| 56. C4×Dic43 | C2×C4 | semidirect |
| 84. C4×D43 | C4⋊C4 | semidirect |
| 116. #384 | D43 | semidirect |
| 119. C43 | #2317 | semidirect |
| 166. C42 | C4×D43 | semidirect |