Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14579188 | C2 | semidirect |
| 2. #19099216 | C2 | semidirect |
| 3. #19099198 | C2 | semidirect |
| 4. #19098806 | C2 | semidirect |
| 5. #19098765 | C2 | semidirect |
| 6. #19098755 | C2 | semidirect |
| 7. #19098712 | C2 | semidirect |
| 8. #19098707 | C2 | semidirect |
| 9. C4×D632 | C2 | semidirect |
| 10. #19098642 | C2 | semidirect |
| 11. #492×C79 | C2 | semidirect |
| 12. C2×#11929625 | C22 | semidirect |
| 18. C2×#11929609 | C22 | semidirect |
| 19. C2×#11929607 | C22 | semidirect |
| 21. #14579137 | C22 | semidirect |
| 28. C4×D316 | C22 | semidirect |
| 30. #14579095 | C22 | semidirect |
| 31. C4⋊(C79⋊C8) | C22 | semidirect |
| 32. #14579085 | C22 | semidirect |
| 34. #14579083 | C22 | semidirect |
| 35. #14579082 | C22 | semidirect |
| 36. (C2×D79)⋊C8 | C22 | semidirect |
| 37. C2×SD16×C79 | C22 | semidirect |
| 38. C2×SD16×C79 | C22 | semidirect |
| 39. C4⋊Q8×C79 | C22 | semidirect |
| 41. C4×C8×C79 | C22 | semidirect |
| 59. D632 | D4 | semidirect |
| 110. D316 | C2×D4 | semidirect |
| 117. C8×C79 | C2×D4 | semidirect |
| 135. C4×C79 | AGL(1,ℤ/8) | semidirect |
| 149. C79 | #3272 | semidirect |
| 153. #492 | D79 | semidirect |
| 166. C2×SD16 | C2×D79 | semidirect |
| 167. C2×SD16 | C2×D79 | semidirect |
| 171. C4⋊Q8 | C2×D79 | semidirect |
| 190. C4×C8 | C2×D79 | semidirect |
| 267. C8 | D4×D79 | semidirect |
| 287. C4 | #14579188 | semidirect |