Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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×#433 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #433 | D47 |
| hypocenter | C47 | #3123 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689735 | C2 | semidirect |
| 3. #15689465 | C2 | semidirect |
| 4. #15689424 | C2 | semidirect |
| 5. #15689329 | C2 | semidirect |
| 7. #15689225 | C2 | semidirect |
| 8. C4×#10625325 | C2 | semidirect |
| 9. C47×#433 | C2 | semidirect |
| 13. #13094024 | C22 | semidirect |
| 15. #13094016 | C22 | semidirect |
| 18. C4×Dic94 | C22 | semidirect |
| 24. #13093958 | C22 | semidirect |
| 25. #13093956 | C22 | semidirect |
| 26. #13093949 | C22 | semidirect |
| 27. #13093949 | C22 | semidirect |
| 31. C4⋊C8×C47 | C22 | semidirect |
| 33. #97×C47 | C22 | semidirect |
| 34. C4×C8×C47 | C22 | semidirect |
| 111. #433 | D47 | semidirect |
| 112. C47 | #3123 | semidirect |
| 130. C4⋊C8 | C2×D47 | semidirect |
| 136. #97 | C2×D47 | semidirect |
| 137. C4×C8 | C2×D47 | semidirect |