Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#493 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #493 | D47 |
| hypocenter | C47 | #3151 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094048 | C2 | semidirect |
| 2. #15689671 | C2 | semidirect |
| 3. #127×D47 | C2 | semidirect |
| 4. #15689511 | C2 | semidirect |
| 5. #15689499 | C2 | semidirect |
| 6. #15689496 | C2 | semidirect |
| 7. #15689495 | C2 | semidirect |
| 8. C4×#10625324 | C2 | semidirect |
| 9. C47×#493 | C2 | semidirect |
| 14. C2×#10625325 | C22 | semidirect |
| 15. C2×#10625335 | C22 | semidirect |
| 16. C2×#10625334 | C22 | semidirect |
| 18. #13094024 | C22 | semidirect |
| 22. #13094011 | C22 | semidirect |
| 26. #13093934 | C22 | semidirect |
| 27. C4×C47⋊C8 | C22 | semidirect |
| 28. C2×D8×C47 | C22 | semidirect |
| 30. #127×C47 | C22 | semidirect |
| 31. C4×C8×C47 | C22 | semidirect |
| 60. #10625324 | D4 | semidirect |
| 85. C8×C47 | C2×D4 | semidirect |
| 86. C47⋊C8 | C2×D4 | semidirect |
| 97. C4×C47 | AGL(1,ℤ/8) | semidirect |
| 114. #493 | D47 | semidirect |
| 118. C47 | #3151 | semidirect |
| 126. C2×D8 | C2×D47 | semidirect |
| 133. #127 | C2×D47 | semidirect |
| 140. C4×C8 | C2×D47 | semidirect |
| 195. C8 | D4×D47 | semidirect |
| 209. C4 | #13094048 | semidirect |