Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 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×C22⋊D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | D42×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | D42 | D71 |
| hypocenter | C71 | #3325 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986714 | C2 | semidirect |
| 2. #17986345 | C2 | semidirect |
| 3. #17986320 | C2 | semidirect |
| 4. #17986289 | C2 | semidirect |
| 5. #17986250 | C2 | semidirect |
| 6. #17986191 | C2 | semidirect |
| 7. #17986133 | C2 | semidirect |
| 8. C4×#11765850 | C2 | semidirect |
| 9. #17986077 | C2 | semidirect |
| 10. #17986004 | C2 | semidirect |
| 11. D42×C71 | C2 | semidirect |
| 13. C2×#11765850 | C22 | semidirect |
| 14. C2×#11765849 | C22 | semidirect |
| 15. #14556128 | C22 | semidirect |
| 17. #14556102 | C22 | semidirect |
| 19. C4×D284 | C22 | semidirect |
| 20. #14556087 | C22 | semidirect |
| 22. #14556061 | C22 | semidirect |
| 23. #14556059 | C22 | semidirect |
| 24. C4⋊(C71⋊C8) | C22 | semidirect |
| 27. #14556049 | C22 | semidirect |
| 28. #14556049 | C22 | semidirect |
| 29. #14556049 | C22 | semidirect |
| 30. #14556048 | C22 | semidirect |
| 31. C22⋊(C71⋊C8) | C22 | semidirect |
| 32. C4×C71⋊C8 | C22 | semidirect |
| 141. C71 | #3325 | semidirect |
| 143. D42 | D71 | semidirect |