Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C22×C8 |
| Fitting | C43×#336 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | #1984 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. C2×Dic86 | C8 | semidirect |
| 38. C2×C8×C43 | Q8 | semidirect |
| 53. C2×C43⋊C8 | Q8 | semidirect |
| 116. C43 | #1984 | semidirect |
| 153. C2×C8 | Dic86 | semidirect |