Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14582778 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#568 | C2 |
| socle | C2×C43 | #386 |
| hypercenter | #568 | D43 |
| hypocenter | C43 | #1903 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582916 | C2 | semidirect |
| 3. #14582905 | C2 | semidirect |
| 4. C2×#13063241 | C2 | semidirect |
| 5. #14582671 | C2 | semidirect |
| 6. C43⋊#338 | C2 | semidirect |
| 7. C43×#568 | C2 | semidirect |
| 11. C2×#10621884 | C4 | semidirect |
| 12. C2×#10621882 | C4 | semidirect |
| 114. #568 | D43 | semidirect |
| 120. C43 | #1903 | semidirect |