Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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 | C2 | D4×C22⋊D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#578 | C2 |
| socle | C2×C43 | D42 |
| hypercenter | #578 | D43 |
| hypocenter | C43 | #3290 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #578 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583707 | C2 | semidirect |
| 2. #14583701 | C2 | semidirect |
| 3. #14583284 | C2 | semidirect |
| 4. #14583171 | C2 | semidirect |
| 5. #14583169 | C2 | semidirect |
| 6. #14583164 | C2 | semidirect |
| 7. #14583075 | C2 | semidirect |
| 8. #14583072 | C2 | semidirect |
| 9. #14583016 | C2 | semidirect |
| 10. #14583014 | C2 | semidirect |
| 11. C43×#578 | C2 | semidirect |
| 18. #13063350 | C22 | semidirect |
| 23. C2×#10621884 | C22 | semidirect |
| 26. #13063332 | C22 | semidirect |
| 28. #13063314 | C22 | semidirect |
| 29. #13063261 | C22 | semidirect |
| 30. #13063260 | C22 | semidirect |
| 31. #13063252 | C22 | semidirect |
| 32. #13063252 | C22 | semidirect |
| 34. #13063244 | C22 | semidirect |
| 35. #13063241 | C22 | semidirect |
| 36. C8×Dic43 | C22 | semidirect |
| 37. 2−1+4×C43 | C22 | semidirect |
| 39. #137×C43 | C22 | semidirect |
| 43. C2×Q16×C43 | C22 | semidirect |
| 44. #131×C43 | C22 | semidirect |
| 150. #578 | D43 | semidirect |
| 161. C43 | #3290 | semidirect |
| 162. 2−1+4 | C2×D43 | semidirect |
| 167. #137 | C2×D43 | semidirect |
| 178. C2×Q16 | C2×D43 | semidirect |
| 185. #131 | C2×D43 | semidirect |