Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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 | #3568 |
| 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. #15689873 | C2 | semidirect |
| 2. #15689842 | C2 | semidirect |
| 3. #15689804 | C2 | semidirect |
| 4. #15689737 | C2 | semidirect |
| 5. #15689708 | C2 | semidirect |
| 6. #15689652 | C2 | semidirect |
| 7. C47×H(3,𝔽4) | C2 | semidirect |
| 8. #13094022 | C22 | semidirect |
| 9. #13094018 | C22 | semidirect |
| 10. #13094017 | C22 | semidirect |
| 11. #13094017 | C22 | semidirect |
| 12. #13094017 | C22 | semidirect |
| 13. #13094017 | C22 | semidirect |
| 14. #13094016 | C22 | semidirect |
| 16. #13094010 | C22 | semidirect |
| 17. #13094006 | C22 | semidirect |
| 20. #13094001 | C22 | semidirect |
| 21. #13094001 | C22 | semidirect |
| 22. #13094001 | C22 | semidirect |
| 23. #13094000 | C22 | semidirect |
| 26. #13093993 | C22 | semidirect |
| 27. Q8×Dic47 | C22 | semidirect |
| 28. C4×Dic94 | C22 | semidirect |
| 31. (C22⋊D47)⋊C4 | C22 | semidirect |
| 32. #13093980 | C22 | semidirect |
| 33. #13093980 | C22 | semidirect |
| 34. C2×C22⋊Dic47 | C22 | semidirect |
| 35. C42×D47 | C22 | semidirect |
| 102. H(3,𝔽4) | D47 | semidirect |
| 108. C47 | #3568 | semidirect |