Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#436 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #436 | D47 |
| hypocenter | C47 | #3324 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689843 | C2 | semidirect |
| 3. #15689470 | C2 | semidirect |
| 4. #15689448 | C2 | semidirect |
| 5. #15689404 | C2 | semidirect |
| 6. #15689369 | C2 | semidirect |
| 7. #15689324 | C2 | semidirect |
| 8. #15689276 | C2 | semidirect |
| 9. C4×#10625325 | C2 | semidirect |
| 10. #15689129 | C2 | semidirect |
| 11. C47×#436 | C2 | semidirect |
| 15. C2×#10625325 | C22 | semidirect |
| 16. #13094024 | C22 | semidirect |
| 20. #13094003 | C22 | semidirect |
| 24. C4×Dic94 | C22 | semidirect |
| 27. #13093983 | C22 | semidirect |
| 28. #13093958 | C22 | semidirect |
| 29. #13093956 | C22 | semidirect |
| 30. #13093949 | C22 | semidirect |
| 33. #13093946 | C22 | semidirect |
| 34. #13093946 | C22 | semidirect |
| 35. #13093946 | C22 | semidirect |
| 36. C2×M16×C47 | C22 | semidirect |
| 38. C4⋊C8×C47 | C22 | semidirect |
| 39. C22⋊C8×C47 | C22 | semidirect |
| 40. C4×C8×C47 | C22 | semidirect |
| 145. #436 | D47 | semidirect |
| 147. C47 | #3324 | semidirect |
| 152. C2×M16 | C2×D47 | semidirect |
| 168. C4⋊C8 | C2×D47 | semidirect |
| 175. C22⋊C8 | C2×D47 | semidirect |
| 176. C4×C8 | C2×D47 | semidirect |