Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#459 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #459 | D43 |
| hypocenter | C43 | #3358 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583569 | C2 | semidirect |
| 2. D4×Dic86 | C2 | semidirect |
| 3. #14583245 | C2 | semidirect |
| 4. #14583244 | C2 | semidirect |
| 5. #14583180 | C2 | semidirect |
| 6. #14583177 | C2 | semidirect |
| 7. #14583092 | C2 | semidirect |
| 8. #14583023 | C2 | semidirect |
| 9. D8×Dic43 | C2 | semidirect |
| 10. C4×#10621882 | C2 | semidirect |
| 11. C43×#459 | C2 | semidirect |
| 83. D4×C43 | #41 | semidirect |
| 102. Dic86 | D8 | semidirect |
| 139. #459 | D43 | semidirect |
| 143. C43 | #3358 | semidirect |
| 222. D4 | #10621900 | semidirect |