Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C24×C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | #2280 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063284 | C2 | semidirect |
| 2. #14582762 | C2 | semidirect |
| 3. #14582759 | C2 | semidirect |
| 5. C4×C22⋊Dic43 | C2 | semidirect |
| 8. C2×C4⋊Dic43 | C22 | semidirect |
| 11. C2×C4×Dic43 | C22 | semidirect |
| 12. C43⋊#95 | C22 | semidirect |
| 15. C23×C4×C43 | C4 | semidirect |
| 57. C2×C4×C43 | C22⋊C4 | semidirect |
| 72. C22×C43 | #117 | semidirect |
| 92. C43 | #2280 | semidirect |
| 95. C23×C4 | Dic43 | semidirect |
| 145. C2×C4 | C22⋊Dic43 | semidirect |
| 158. C22 | #13063284 | semidirect |