Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#390 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2375 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582799 | C2 | semidirect |
| 3. #14582790 | C2 | semidirect |
| 4. #14582789 | C2 | semidirect |
| 5. #14582787 | C2 | semidirect |
| 6. #14582779 | C2 | semidirect |
| 7. #14582776 | C2 | semidirect |
| 8. #14582754 | C2 | semidirect |
| 9. C43×#390 | C2 | semidirect |
| 12. C23×Dic43 | C22 | semidirect |
| 13. #13063293 | C4 | semidirect |
| 14. C2×Dic43⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic43 | C22 | semidirect |
| 23. C2×C4×Dic43 | C22 | semidirect |
| 24. C43⋊#95 | C22 | semidirect |
| 25. C43⋊#95 | C22 | semidirect |
| 26. C43⋊#95 | C22 | semidirect |
| 28. C2×C4⋊C4×C43 | C22 | semidirect |
| 30. C2×C22⋊C4×C43 | C22 | semidirect |
| 31. C2×C42×C43 | C22 | semidirect |
| 38. C23×D43 | C2×C4 | semidirect |
| 60. C22⋊Dic43 | C2×C4 | semidirect |
| 65. (C2×D43)⋊C4 | C2×C4 | semidirect |
| 152. #390 | D43 | semidirect |
| 159. C43 | #2375 | semidirect |
| 166. C2×C4⋊C4 | C2×D43 | semidirect |
| 176. C2×C22⋊C4 | C2×D43 | semidirect |
| 178. C2×C42 | C2×D43 | semidirect |