Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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 | #3549 |
| 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. #14583641 | C2 | semidirect |
| 2. #14583611 | C2 | semidirect |
| 3. #14583531 | C2 | semidirect |
| 4. #14583467 | C2 | semidirect |
| 5. #14583464 | C2 | semidirect |
| 6. #14583448 | C2 | semidirect |
| 7. C43×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#10621902 | C22 | semidirect |
| 9. C2×#10621900 | C22 | semidirect |
| 10. C22×C22⋊D43 | C22 | semidirect |
| 11. C2×D4×D43 | C22 | semidirect |
| 12. #13063323 | C22 | semidirect |
| 13. #13063322 | C22 | semidirect |
| 15. #13063321 | C22 | semidirect |
| 16. #13063314 | C22 | semidirect |
| 17. #13063313 | C22 | semidirect |
| 18. #13063311 | C22 | semidirect |
| 19. #13063298 | C22 | semidirect |
| 20. #13063298 | C22 | semidirect |
| 21. #13063297 | C22 | semidirect |
| 22. #13063295 | C22 | semidirect |
| 23. #13063295 | C22 | semidirect |
| 24. #13063294 | C22 | semidirect |
| 25. #13063293 | C22 | semidirect |
| 26. (C22⋊D43)⋊C4 | C22 | semidirect |
| 27. #13063282 | C22 | semidirect |
| 28. #13063281 | C22 | semidirect |
| 29. C42×D43 | C22 | semidirect |
| 30. #124×C43 | C22 | semidirect |
| 31. #124×C43 | C22 | semidirect |
| 32. #120×C43 | C22 | semidirect |
| 103. H(3,𝔽4) | D43 | semidirect |
| 109. C43 | #3549 | semidirect |
| 121. #124 | C2×D43 | semidirect |
| 122. #124 | C2×D43 | semidirect |
| 130. #120 | C2×D43 | semidirect |