Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | D42×C47 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | D42 | D47 |
| hypocenter | C47 | #3325 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689838 | C2 | semidirect |
| 2. #15689469 | C2 | semidirect |
| 3. #15689444 | C2 | semidirect |
| 4. #15689413 | C2 | semidirect |
| 5. #15689374 | C2 | semidirect |
| 6. #15689315 | C2 | semidirect |
| 7. #15689257 | C2 | semidirect |
| 8. C4×#10625334 | C2 | semidirect |
| 9. #15689201 | C2 | semidirect |
| 10. #15689128 | C2 | semidirect |
| 11. D42×C47 | C2 | semidirect |
| 13. C2×#10625334 | C22 | semidirect |
| 14. C2×#10625329 | C22 | semidirect |
| 15. #13094024 | C22 | semidirect |
| 17. #13093998 | C22 | semidirect |
| 19. C4×D188 | C22 | semidirect |
| 20. #13093983 | C22 | semidirect |
| 22. #13093957 | C22 | semidirect |
| 23. #13093955 | C22 | semidirect |
| 24. C4⋊(C47⋊C8) | C22 | semidirect |
| 27. #13093945 | C22 | semidirect |
| 28. #13093945 | C22 | semidirect |
| 29. #13093945 | C22 | semidirect |
| 30. #13093944 | C22 | semidirect |
| 31. C22⋊(C47⋊C8) | C22 | semidirect |
| 32. C4×C47⋊C8 | C22 | semidirect |
| 142. D42 | D47 | semidirect |
| 152. C47 | #3325 | semidirect |