Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
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×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D47 |
| hypocenter | C47 | #3549 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689865 | C2 | semidirect |
| 2. #15689835 | C2 | semidirect |
| 3. #15689755 | C2 | semidirect |
| 4. #15689691 | C2 | semidirect |
| 5. #15689688 | C2 | semidirect |
| 6. #15689672 | C2 | semidirect |
| 7. C47×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#10625354 | C22 | semidirect |
| 9. C2×#10625352 | C22 | semidirect |
| 10. C22×C22⋊D47 | C22 | semidirect |
| 11. C2×D4×D47 | C22 | semidirect |
| 12. #13094022 | C22 | semidirect |
| 13. #13094021 | C22 | semidirect |
| 15. #13094020 | C22 | semidirect |
| 16. #13094013 | C22 | semidirect |
| 17. #13094012 | C22 | semidirect |
| 18. #13094010 | C22 | semidirect |
| 19. #13093997 | C22 | semidirect |
| 20. #13093997 | C22 | semidirect |
| 21. #13093996 | C22 | semidirect |
| 22. #13093994 | C22 | semidirect |
| 23. #13093994 | C22 | semidirect |
| 24. #13093993 | C22 | semidirect |
| 25. #13093992 | C22 | semidirect |
| 26. (C22⋊D47)⋊C4 | C22 | semidirect |
| 27. #13093981 | C22 | semidirect |
| 28. #13093980 | C22 | semidirect |
| 29. C42×D47 | C22 | semidirect |
| 30. #124×C47 | C22 | semidirect |
| 31. #124×C47 | C22 | semidirect |
| 32. #120×C47 | C22 | semidirect |
| 103. H(3,𝔽4) | D47 | semidirect |
| 109. C47 | #3549 | semidirect |
| 121. #124 | C2×D47 | semidirect |
| 122. #124 | C2×D47 | semidirect |
| 130. #120 | C2×D47 | semidirect |