Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#519 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #519 | D47 |
| hypocenter | C47 | #2949 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15689221 | C2 | semidirect |
| 4. C4×#10625336 | C2 | semidirect |
| 5. #15689159 | C2 | semidirect |
| 6. #15689132 | C2 | semidirect |
| 8. #15689079 | C2 | semidirect |
| 9. C47×#519 | C2 | semidirect |
| 11. C2×#10625336 | C4 | semidirect |
| 20. #13093957 | C22 | semidirect |
| 21. #13093955 | C22 | semidirect |
| 22. #13093948 | C22 | semidirect |
| 24. #13093935 | C22 | semidirect |
| 25. C4×C47⋊C8 | C22 | semidirect |
| 28. C4×Q8×C47 | C22 | semidirect |
| 35. C2×Q8×C47 | C2×C4 | semidirect |
| 53. #10625336 | C2×C4 | semidirect |
| 54. #10625336 | C2×C4 | semidirect |
| 59. C2×C47⋊C8 | C2×C4 | semidirect |
| 105. #519 | D47 | semidirect |
| 113. C47 | #2949 | semidirect |
| 122. C4×Q8 | C2×D47 | semidirect |
| 139. C2×Q8 | C4×D47 | semidirect |