Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #2376 |
| 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. #14582794 | C2 | semidirect |
| 3. #14582793 | C2 | semidirect |
| 4. #14582787 | C2 | semidirect |
| 5. #14582783 | C2 | semidirect |
| 7. #14582771 | C2 | semidirect |
| 8. #14582757 | C2 | semidirect |
| 12. #13063306 | C4 | semidirect |
| 44. C22×Dic43 | C2×C4 | semidirect |
| 56. C22⋊Dic43 | C2×C4 | semidirect |
| 60. Dic43⋊C4 | C2×C4 | semidirect |
| 136. C43 | #2376 | semidirect |