Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17986633 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #472×C71 | C2 |
| socle | C2×C71 | D42 |
| hypercenter | #472 | D71 |
| hypocenter | C71 | #3290 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986816 | C2 | semidirect |
| 2. #17986809 | C2 | semidirect |
| 3. #17986800 | C2 | semidirect |
| 4. #17986382 | C2 | semidirect |
| 5. #17986275 | C2 | semidirect |
| 6. #17986261 | C2 | semidirect |
| 7. #17986179 | C2 | semidirect |
| 8. #17986170 | C2 | semidirect |
| 9. #17986115 | C2 | semidirect |
| 10. #17986114 | C2 | semidirect |
| 11. #472×C71 | C2 | semidirect |
| 12. #14556175 | C22 | semidirect |
| 16. #14556161 | C22 | semidirect |
| 27. C2×Dic284 | C22 | semidirect |
| 28. C2×#11765853 | C22 | semidirect |
| 31. #14556136 | C22 | semidirect |
| 33. #14556115 | C22 | semidirect |
| 34. #14556063 | C22 | semidirect |
| 35. #14556055 | C22 | semidirect |
| 37. #14556054 | C22 | semidirect |
| 38. #14556046 | C22 | semidirect |
| 39. C8×Dic71 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C71 | C22 | semidirect |
| 42. #131×C71 | C22 | semidirect |
| 43. #108×C71 | C22 | semidirect |
| 44. #100×C71 | C22 | semidirect |
| 150. C71 | #3290 | semidirect |
| 156. #472 | D71 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D71 | semidirect |
| 185. #131 | C2×D71 | semidirect |
| 188. #108 | C2×D71 | semidirect |
| 193. #100 | C2×D71 | semidirect |