Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 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 | 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 | #3205 |
| 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. #15689671 | C2 | semidirect |
| 2. #127×D47 | C2 | semidirect |
| 3. #15689499 | C2 | semidirect |
| 4. #15689470 | C2 | semidirect |
| 5. #15689469 | C2 | semidirect |
| 6. #15689316 | C2 | semidirect |
| 7. #15689255 | C2 | semidirect |
| 8. #15689174 | C2 | semidirect |
| 9. C47×#493 | C2 | semidirect |
| 14. C2×#10625334 | C22 | semidirect |
| 15. #13094024 | C22 | semidirect |
| 24. D4×Dic47 | C22 | semidirect |
| 26. Dic47⋊C8 | C22 | semidirect |
| 27. #13093946 | C22 | semidirect |
| 28. #13093945 | C22 | semidirect |
| 30. C4×C47⋊C8 | C22 | semidirect |
| 31. C2×D8×C47 | C22 | semidirect |
| 33. #127×C47 | C22 | semidirect |
| 34. C4×C8×C47 | C22 | semidirect |
| 100. C4×D47 | D8 | semidirect |
| 136. #493 | D47 | semidirect |
| 142. C47 | #3205 | semidirect |
| 148. C2×D8 | C2×D47 | semidirect |
| 155. #127 | C2×D47 | semidirect |
| 167. C4×C8 | C2×D47 | semidirect |