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×C22⋊D71 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | #585×C71 | C2 |
| socle | C2×C71 | C23×D4 |
| hypercenter | #585 | D71 |
| hypocenter | C71 | #3586 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556175 | C2 | semidirect |
| 2. #17986814 | C2 | semidirect |
| 3. #17986810 | C2 | semidirect |
| 4. #17986797 | C2 | semidirect |
| 5. C2×#14556158 | C2 | semidirect |
| 6. #17986766 | C2 | semidirect |
| 7. #585×C71 | C2 | semidirect |
| 9. #14556175 | C22 | semidirect |
| 10. C2×#11765865 | C22 | semidirect |
| 12. C22×Dic142 | C22 | semidirect |
| 14. #14556159 | C22 | semidirect |
| 15. #14556158 | C22 | semidirect |
| 16. #14556158 | C22 | semidirect |
| 17. #14556154 | C22 | semidirect |
| 18. #14556153 | C22 | semidirect |
| 19. #14556148 | C22 | semidirect |
| 20. C2×#11765855 | C22 | semidirect |
| 21. C2×#11765853 | C22 | semidirect |
| 22. #14556135 | C22 | semidirect |
| 23. C2×#11765849 | C22 | semidirect |
| 25. 2−1+4×C71 | C22 | semidirect |
| 27. H(5,𝔽2)×C71 | C22 | semidirect |
| 113. C71 | #3586 | semidirect |
| 114. #585 | D71 | semidirect |
| 124. 2−1+4 | C2×D71 | semidirect |
| 126. H(5,𝔽2) | C2×D71 | semidirect |