Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
564 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 147 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×#399 | C2 |
| hypercenter | #399 | D43 |
| hypocenter | C43 | #2580 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063290 | C2 | semidirect |
| 3. #14582834 | C2 | semidirect |
| 4. #14582812 | C2 | semidirect |
| 5. #14582811 | C2 | semidirect |
| 7. #14582794 | C2 | semidirect |
| 8. #14582771 | C2 | semidirect |
| 9. #14582770 | C2 | semidirect |
| 10. #14582763 | C2 | semidirect |
| 11. C43×#399 | C2 | semidirect |
| 45. C2×C22⋊D43 | Q8 | semidirect |
| 144. #399 | D43 | semidirect |
| 152. C43 | #2580 | semidirect |