Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14582776 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#418 | C2 |
| socle | C2×C43 | #386 |
| hypercenter | #418 | D43 |
| hypocenter | C43 | #1904 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583374 | C2 | semidirect |
| 3. #14582915 | C2 | semidirect |
| 4. #14582872 | C2 | semidirect |
| 5. #14582671 | C2 | semidirect |
| 6. #14582655 | C2 | semidirect |
| 7. C43×#418 | C2 | semidirect |
| 11. C2×#10621883 | C4 | semidirect |
| 12. C2×#10621882 | C4 | semidirect |
| 39. C2×D172 | C2×C4 | semidirect |
| 41. C2×Dic86 | C2×C4 | semidirect |
| 59. C2×C43⋊C8 | C2×C4 | semidirect |
| 119. #418 | D43 | semidirect |
| 123. C43 | #1904 | semidirect |