Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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×#381 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #381 | D43 |
| hypocenter | C43 | #2283 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582766 | C2 | semidirect |
| 3. #14582763 | C2 | semidirect |
| 6. #14582750 | C2 | semidirect |
| 8. #14582744 | C2 | semidirect |
| 14. C2×C4×Dic43 | C4 | semidirect |
| 108. C43 | #2283 | semidirect |