Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 317 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C24×C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | C22⋊#95 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43⋊#95 | C2 | semidirect |
| 7. C2×C22⋊Dic43 | C4 | semidirect |
| 12. C23×C4×C43 | C4 | semidirect |
| 33. C22×Dic43 | C2×C4 | semidirect |
| 58. C2×C4×C43 | C22⋊C4 | semidirect |
| 70. C22×C43 | #95 | semidirect |
| 97. C43 | C22⋊#95 | semidirect |
| 102. C23×C4 | Dic43 | semidirect |
| 157. C2×C4 | C22⋊Dic43 | semidirect |
| 164. C22 | C43⋊#95 | semidirect |