Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#493 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #493 | D47 |
| hypocenter | C47 | #3155 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094048 | C2 | semidirect |
| 2. C2×#13094043 | C2 | semidirect |
| 3. C2×D8×D47 | C2 | semidirect |
| 4. #15689686 | C2 | semidirect |
| 5. #15689511 | C2 | semidirect |
| 6. #15689510 | C2 | semidirect |
| 7. #15689507 | C2 | semidirect |
| 8. #15689506 | C2 | semidirect |
| 9. #15689498 | C2 | semidirect |
| 10. #15689077 | C2 | semidirect |
| 11. C47×#493 | C2 | semidirect |
| 16. C2×Dic188 | C22 | semidirect |
| 17. C2×#10625325 | C22 | semidirect |
| 18. C2×#10625335 | C22 | semidirect |
| 19. C2×#10625335 | C22 | semidirect |
| 22. C2×#10625334 | C22 | semidirect |
| 26. #13094020 | C22 | semidirect |
| 27. #13094012 | C22 | semidirect |
| 28. #13094011 | C22 | semidirect |
| 32. #13093935 | C22 | semidirect |
| 33. #13093934 | C22 | semidirect |
| 34. C8×Dic47 | C22 | semidirect |
| 36. C2×D8×C47 | C22 | semidirect |
| 37. C2×D8×C47 | C22 | semidirect |
| 38. #127×C47 | C22 | semidirect |
| 39. C4×C8×C47 | C22 | semidirect |
| 75. #10625324 | D4 | semidirect |
| 76. C8×D47 | D4 | semidirect |
| 139. #493 | D47 | semidirect |
| 141. C47 | #3155 | semidirect |
| 155. C2×D8 | C2×D47 | semidirect |
| 156. C2×D8 | C2×D47 | semidirect |
| 160. #127 | C2×D47 | semidirect |
| 169. C4×C8 | C2×D47 | semidirect |