Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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×#390 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | C4×#124 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063290 | C2 | semidirect |
| 4. #14582805 | C2 | semidirect |
| 5. #14582787 | C2 | semidirect |
| 6. #14582764 | C2 | semidirect |
| 7. C22⋊C4×Dic43 | C2 | semidirect |
| 8. C42×Dic43 | C2 | semidirect |
| 12. #13063312 | C4 | semidirect |
| 46. C2×Dic86 | C2×C4 | semidirect |
| 51. C22⋊Dic43 | C2×C4 | semidirect |
| 57. C4×Dic43 | C2×C4 | semidirect |
| 105. Dic43 | #124 | semidirect |
| 122. C43 | C4×#124 | semidirect |