Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | #543×C71 | C2 |
| hypercenter | #543 | D71 |
| hypocenter | C71 | #3459 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986598 | C2 | semidirect |
| 2. #17986589 | C2 | semidirect |
| 3. #17986561 | C2 | semidirect |
| 4. #17986535 | C2 | semidirect |
| 5. #17986512 | C2 | semidirect |
| 6. C2×(C22⋊D71)⋊C4 | C2 | semidirect |
| 7. #543×C71 | C2 | semidirect |
| 8. C2×#11765866 | C22 | semidirect |
| 11. C22×C4×D71 | C22 | semidirect |
| 12. #14556123 | C22 | semidirect |
| 13. #14556119 | C22 | semidirect |
| 14. #14556117 | C22 | semidirect |
| 15. #14556113 | C22 | semidirect |
| 16. #14556112 | C22 | semidirect |
| 17. #14556104 | C22 | semidirect |
| 18. #14556103 | C22 | semidirect |
| 21. #14556098 | C22 | semidirect |
| 22. Q8×Dic71 | C22 | semidirect |
| 23. #14556090 | C22 | semidirect |
| 24. (C22⋊D71)⋊C4 | C22 | semidirect |
| 25. (C22⋊D71)⋊C4 | C22 | semidirect |
| 26. #14556086 | C22 | semidirect |
| 27. C2×Dic71⋊C4 | C22 | semidirect |
| 28. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 29. C2×C4×Dic71 | C22 | semidirect |
| 30. C22⋊Q8×C71 | C22 | semidirect |
| 31. C22⋊Q8×C71 | C22 | semidirect |
| 64. C23×C71 | #41 | semidirect |
| 107. C71 | #3459 | semidirect |
| 108. #543 | D71 | semidirect |
| 125. C22⋊Q8 | C2×D71 | semidirect |
| 126. C22⋊Q8 | C2×D71 | semidirect |
| 175. C23 | #11765866 | semidirect |