Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556153 | C2 | semidirect |
| 2. D4×D284 | C2 | semidirect |
| 3. #17986375 | C2 | semidirect |
| 4. #17986250 | C2 | semidirect |
| 5. #17986199 | C2 | semidirect |
| 6. #17986191 | C2 | semidirect |
| 7. #17986144 | C2 | semidirect |
| 8. #17986132 | C2 | semidirect |
| 9. C4×#11765852 | C2 | semidirect |
| 10. #17986077 | C2 | semidirect |
| 11. #550×C71 | C2 | semidirect |
| 16. C2×#11765852 | C22 | semidirect |
| 18. C2×#11765850 | C22 | semidirect |
| 19. C2×#11765850 | C22 | semidirect |
| 20. C2×#11765849 | C22 | semidirect |
| 26. #14556059 | C22 | semidirect |
| 27. C4⋊(C71⋊C8) | C22 | semidirect |
| 28. #14556052 | C22 | semidirect |
| 29. #14556049 | C22 | semidirect |
| 31. #14556048 | C22 | semidirect |
| 32. C22⋊(C71⋊C8) | C22 | semidirect |
| 33. C4×C71⋊C8 | C22 | semidirect |
| 34. C2×#41×C71 | C22 | semidirect |
| 36. #127×C71 | C22 | semidirect |
| 38. #121×C71 | C22 | semidirect |
| 39. C4×Q8×C71 | C22 | semidirect |
| 54. #11765852 | D4 | semidirect |
| 91. Q8×C71 | C2×D4 | semidirect |
| 120. C71⋊C8 | C2×D4 | semidirect |
| 139. C4×C71 | AGL(1,ℤ/8) | semidirect |
| 151. C71 | #3274 | semidirect |
| 153. #550 | D71 | semidirect |
| 163. C2×#41 | C2×D71 | semidirect |
| 175. #127 | C2×D71 | semidirect |
| 179. #121 | C2×D71 | semidirect |
| 181. C4×Q8 | C2×D71 | semidirect |
| 242. Q8 | D4×D71 | semidirect |
| 291. C4 | #14556153 | semidirect |