Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#424 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #424 | D47 |
| hypocenter | C47 | #3041 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094052 | C2 | semidirect |
| 2. C22×D376 | C2 | semidirect |
| 3. #15689692 | C2 | semidirect |
| 4. #15689597 | C2 | semidirect |
| 5. #15689339 | C2 | semidirect |
| 6. #15689319 | C2 | semidirect |
| 7. #15689129 | C2 | semidirect |
| 8. #15689120 | C2 | semidirect |
| 9. C47×#424 | C2 | semidirect |
| 14. C2×#10625325 | C22 | semidirect |
| 17. C2×D376 | C22 | semidirect |
| 18. #13094021 | C22 | semidirect |
| 19. #13094012 | C22 | semidirect |
| 22. C4×D188 | C22 | semidirect |
| 26. #13093949 | C22 | semidirect |
| 27. #13093946 | C22 | semidirect |
| 28. #13093946 | C22 | semidirect |
| 32. C4⋊C8×C47 | C22 | semidirect |
| 45. C2×D188 | D4 | semidirect |
| 128. #424 | D47 | semidirect |
| 131. C47 | #3041 | semidirect |
| 151. C4⋊C8 | C2×D47 | semidirect |