Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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. #135×D79 | C2 | semidirect |
| 2. #19098996 | C2 | semidirect |
| 3. #19098995 | C2 | semidirect |
| 4. #19098994 | C2 | semidirect |
| 5. #19098993 | C2 | semidirect |
| 6. #19098992 | C2 | semidirect |
| 7. Q32×D79 | C2 | semidirect |
| 8. SD32×D79 | C2 | semidirect |
| 9. D16×D79 | C2 | semidirect |
| 10. C2×C16×D79 | C2 | semidirect |
| 11. #508×C79 | C2 | semidirect |
| 13. #14579184 | C22 | semidirect |
| 14. #14579183 | C22 | semidirect |
| 17. #14579180 | C22 | semidirect |
| 22. Dic632 | C22 | semidirect |
| 23. #14579107 | C22 | semidirect |
| 24. #14579106 | C22 | semidirect |
| 25. #14579105 | C22 | semidirect |
| 26. #14579104 | C22 | semidirect |
| 27. D1264 | C22 | semidirect |
| 28. #14579102 | C22 | semidirect |
| 29. C2×C79⋊C16 | C22 | semidirect |
| 32. C16×D79 | C22 | semidirect |
| 33. C16×D79 | C22 | semidirect |
| 34. #135×C79 | C22 | semidirect |
| 35. Q32×C79 | C22 | semidirect |
| 36. SD32×C79 | C22 | semidirect |
| 37. D16×C79 | C22 | semidirect |
| 38. C2×C16×C79 | C22 | semidirect |
| 115. D79 | #508 | direct (N × H) |
| 117. C79 | C2×#508 | semidirect |
| 124. #508 | D79 | direct (N × H) |
| 135. #135 | C2×D79 | semidirect |
| 142. Q32 | C2×D79 | semidirect |
| 146. SD32 | C2×D79 | semidirect |
| 149. D16 | C2×D79 | semidirect |
| 155. C2×C16 | C2×D79 | semidirect |