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×#379 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #379 | D43 |
| hypocenter | C43 | #2375 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582799 | C2 | semidirect |
| 3. #14582793 | C2 | semidirect |
| 4. #14582787 | C2 | semidirect |
| 5. #14582775 | C2 | semidirect |
| 6. #14582755 | C2 | semidirect |
| 7. C43×#379 | C2 | semidirect |
| 9. C22×C4×D43 | C22 | semidirect |
| 10. #13063294 | C4 | semidirect |
| 11. C2×Dic43⋊C4 | C22 | semidirect |
| 15. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic43 | C22 | semidirect |
| 17. C43⋊#95 | C22 | semidirect |
| 18. C43⋊#95 | C22 | semidirect |
| 24. C24×C43 | C2×C4 | semidirect |
| 40. C22⋊Dic43 | C2×C4 | semidirect |
| 102. #379 | D43 | semidirect |
| 103. C43 | #2375 | semidirect |
| 121. C24 | C4×D43 | semidirect |