Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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 | C22×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#432 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #432 | D47 |
| hypocenter | C47 | #3217 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094021 | C2 | semidirect |
| 2. #15689657 | C2 | semidirect |
| 3. #15689512 | C2 | semidirect |
| 4. #15689488 | C2 | semidirect |
| 5. #15689324 | C2 | semidirect |
| 6. #15689319 | C2 | semidirect |
| 7. #15689276 | C2 | semidirect |
| 8. #15689259 | C2 | semidirect |
| 9. C47×#432 | C2 | semidirect |
| 13. C2×#10625325 | C22 | semidirect |
| 14. C2×D376 | C22 | semidirect |
| 20. #13094016 | C22 | semidirect |
| 21. #13094012 | C22 | semidirect |
| 25. C4×Dic94 | C22 | semidirect |
| 26. C4×D188 | C22 | semidirect |
| 29. #13093946 | C22 | semidirect |
| 30. #13093946 | C22 | semidirect |
| 32. C4⋊C8×C47 | C22 | semidirect |
| 34. #97×C47 | C22 | semidirect |
| 136. #432 | D47 | semidirect |
| 137. C47 | #3217 | semidirect |
| 158. C4⋊C8 | C2×D47 | semidirect |
| 162. #97 | C2×D47 | semidirect |