Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 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 | C22 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#433 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #433 | D43 |
| hypocenter | C43 | #3220 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583504 | C2 | semidirect |
| 2. #14583468 | C2 | semidirect |
| 3. #14583288 | C2 | semidirect |
| 4. #14583276 | C2 | semidirect |
| 5. #14583264 | C2 | semidirect |
| 6. #14583254 | C2 | semidirect |
| 7. #14583115 | C2 | semidirect |
| 8. #14583095 | C2 | semidirect |
| 9. #14583046 | C2 | semidirect |
| 10. #14583035 | C2 | semidirect |
| 11. C43×#433 | C2 | semidirect |
| 14. C2×#10621873 | C22 | semidirect |
| 17. C2×D344 | C22 | semidirect |
| 20. #13063322 | C22 | semidirect |
| 21. #13063317 | C22 | semidirect |
| 29. C4×D172 | C22 | semidirect |
| 30. #13063250 | C22 | semidirect |
| 33. #13063247 | C22 | semidirect |
| 35. C4⋊C8×C43 | C22 | semidirect |
| 37. #97×C43 | C22 | semidirect |
| 38. C4×C8×C43 | C22 | semidirect |
| 139. #433 | D43 | semidirect |
| 140. C43 | #3220 | semidirect |
| 160. C4⋊C8 | C2×D43 | semidirect |
| 166. #97 | C2×D43 | semidirect |
| 167. C4×C8 | C2×D43 | semidirect |