Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×C22⋊D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | D42×C47 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | D42 | D47 |
| hypocenter | C47 | #3274 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094050 | C2 | semidirect |
| 2. #15689794 | C2 | semidirect |
| 3. #15689499 | C2 | semidirect |
| 4. #15689374 | C2 | semidirect |
| 5. #15689320 | C2 | semidirect |
| 6. #15689318 | C2 | semidirect |
| 7. #15689266 | C2 | semidirect |
| 8. #15689257 | C2 | semidirect |
| 9. C4×#10625335 | C2 | semidirect |
| 10. #15689201 | C2 | semidirect |
| 11. D42×C47 | C2 | semidirect |
| 12. C2×#10625350 | C22 | semidirect |
| 15. C2×#10625335 | C22 | semidirect |
| 17. C2×#10625334 | C22 | semidirect |
| 18. C2×#10625334 | C22 | semidirect |
| 19. C2×#10625329 | C22 | semidirect |
| 20. #13094021 | C22 | semidirect |
| 22. #13093998 | C22 | semidirect |
| 24. C4×Dic94 | C22 | semidirect |
| 26. #13093955 | C22 | semidirect |
| 27. C4⋊(C47⋊C8) | C22 | semidirect |
| 28. #13093947 | C22 | semidirect |
| 30. #13093945 | C22 | semidirect |
| 31. #13093944 | C22 | semidirect |
| 32. C22⋊(C47⋊C8) | C22 | semidirect |
| 33. C4×C47⋊C8 | C22 | semidirect |
| 71. #10625335 | D4 | semidirect |
| 117. Dic94 | C2×D4 | semidirect |
| 120. C47⋊C8 | C2×D4 | semidirect |
| 138. C4×C47 | AGL(1,ℤ/8) | semidirect |
| 153. D42 | D47 | semidirect |
| 162. C47 | #3274 | semidirect |
| 291. C4 | #13094050 | semidirect |