Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
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×#14579186 | C2 | semidirect |
| 2. D4×D316 | C2 | semidirect |
| 3. #19098939 | C2 | semidirect |
| 4. #19098814 | C2 | semidirect |
| 5. #19098763 | C2 | semidirect |
| 6. #19098755 | C2 | semidirect |
| 7. #19098708 | C2 | semidirect |
| 8. #19098696 | C2 | semidirect |
| 9. C4×#11929611 | C2 | semidirect |
| 10. #19098641 | C2 | semidirect |
| 11. #550×C79 | C2 | semidirect |
| 16. C2×#11929611 | C22 | semidirect |
| 18. C2×#11929609 | C22 | semidirect |
| 19. C2×#11929609 | C22 | semidirect |
| 20. C2×#11929608 | C22 | semidirect |
| 26. #14579092 | C22 | semidirect |
| 27. C4⋊(C79⋊C8) | C22 | semidirect |
| 28. #14579085 | C22 | semidirect |
| 29. #14579082 | C22 | semidirect |
| 31. #14579081 | C22 | semidirect |
| 32. C22⋊(C79⋊C8) | C22 | semidirect |
| 33. C4×C79⋊C8 | C22 | semidirect |
| 34. C2×#41×C79 | C22 | semidirect |
| 36. #127×C79 | C22 | semidirect |
| 38. #121×C79 | C22 | semidirect |
| 39. C4×Q8×C79 | C22 | semidirect |
| 54. #11929611 | D4 | semidirect |
| 91. Q8×C79 | C2×D4 | semidirect |
| 120. C79⋊C8 | C2×D4 | semidirect |
| 139. C4×C79 | AGL(1,ℤ/8) | semidirect |
| 151. C79 | #3274 | semidirect |
| 153. #550 | D79 | semidirect |
| 163. C2×#41 | C2×D79 | semidirect |
| 175. #127 | C2×D79 | semidirect |
| 179. #121 | C2×D79 | semidirect |
| 181. C4×Q8 | C2×D79 | semidirect |
| 242. Q8 | D4×D79 | semidirect |
| 291. C4 | #14579186 | semidirect |