Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1144 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | C2×#381 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582760 | C2 | direct (N × H) |
| 4. C2×C43⋊#95 | C2 | semidirect |
| 8. C23×Dic43 | C4 | semidirect |
| 14. C43⋊#95 | C22 | semidirect |
| 36. C22×Dic43 | C2×C4 | semidirect |
| 83. C2×C43 | #381 | semidirect |
| 93. C43 | C2×#381 | semidirect |
| 170. C2 | #14582760 | direct (N × H) |