Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D284 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | #568×C71 | C2 |
| socle | C2×C71 | C23×D4 |
| hypercenter | #568 | D71 |
| hypocenter | C71 | #3586 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986835 | C2 | semidirect |
| 2. C2×#14556175 | C2 | semidirect |
| 3. #17986816 | C2 | semidirect |
| 4. #17986811 | C2 | semidirect |
| 5. #17986799 | C2 | semidirect |
| 6. C2×#14556161 | C2 | semidirect |
| 7. #568×C71 | C2 | semidirect |
| 10. #14556175 | C22 | semidirect |
| 11. #14556175 | C22 | semidirect |
| 12. #14556174 | C22 | semidirect |
| 15. C2×#11765865 | C22 | semidirect |
| 18. C22×Dic142 | C22 | semidirect |
| 20. #14556161 | C22 | semidirect |
| 21. #14556161 | C22 | semidirect |
| 22. #14556161 | C22 | semidirect |
| 23. #14556156 | C22 | semidirect |
| 24. #14556156 | C22 | semidirect |
| 25. #14556150 | C22 | semidirect |
| 26. C2×Dic284 | C22 | semidirect |
| 27. C2×#11765854 | C22 | semidirect |
| 29. #131×C71 | C22 | semidirect |
| 30. C2×M16×C71 | C22 | semidirect |
| 113. C71 | #3586 | semidirect |
| 120. #568 | D71 | semidirect |
| 142. #131 | C2×D71 | semidirect |
| 143. C2×M16 | C2×D71 | semidirect |