Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator | C2×C47 | C24×C4 |
| Fitting | C47×#519 | C2 |
| socle | C22×C47 | C25 |
| hypercenter | #519 | D47 |
| hypocenter | C47 | #3428 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689605 | C2 | semidirect |
| 3. #15689601 | C2 | semidirect |
| 4. #15689597 | C2 | semidirect |
| 5. C4×#10625354 | C2 | semidirect |
| 6. #117×D47 | C2 | semidirect |
| 7. C47×#519 | C2 | semidirect |
| 8. C2×#10625354 | C4 | semidirect |
| 13. Q8×Dic47 | C22 | semidirect |
| 14. C4×D188 | C22 | semidirect |
| 15. #13093986 | C22 | semidirect |
| 17. #13093982 | C22 | semidirect |
| 18. #13093981 | C22 | semidirect |
| 20. C4⋊C4×D47 | C22 | semidirect |
| 22. C42×D47 | C22 | semidirect |
| 24. C4×Q8×C47 | C22 | semidirect |
| 27. C2×Q8×C47 | C2×C4 | semidirect |
| 31. #10625354 | C2×C4 | semidirect |
| 32. #10625354 | C2×C4 | semidirect |
| 33. C2×D188 | C2×C4 | semidirect |
| 35. C2×C4×D47 | C2×C4 | semidirect |
| 83. #519 | D47 | semidirect |
| 87. C47 | #3428 | semidirect |
| 95. C4×Q8 | C2×D47 | semidirect |
| 109. C2×Q8 | C4×D47 | semidirect |