Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C43×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D43 |
| hypocenter | C43 | #3529 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583649 | C2 | semidirect |
| 2. #14583643 | C2 | semidirect |
| 3. #14583638 | C2 | semidirect |
| 4. #14583448 | C2 | semidirect |
| 5. #14583428 | C2 | semidirect |
| 6. #14583405 | C2 | semidirect |
| 7. C43×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#10621902 | C22 | semidirect |
| 10. C23×Dic43 | C22 | semidirect |
| 11. #13063323 | C22 | semidirect |
| 13. #13063318 | C22 | semidirect |
| 14. #13063317 | C22 | semidirect |
| 15. #13063313 | C22 | semidirect |
| 16. #13063309 | C22 | semidirect |
| 17. #13063307 | C22 | semidirect |
| 19. #13063302 | C22 | semidirect |
| 20. #13063301 | C22 | semidirect |
| 21. #13063298 | C22 | semidirect |
| 24. #13063294 | C22 | semidirect |
| 25. Q8×Dic43 | C22 | semidirect |
| 27. (C22⋊D43)⋊C4 | C22 | semidirect |
| 28. #13063281 | C22 | semidirect |
| 29. C42×D43 | C22 | semidirect |
| 100. H(3,𝔽4) | D43 | semidirect |
| 105. C43 | #3529 | semidirect |