Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 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×#14579185 | C2 | semidirect |
| 2. #19099233 | C2 | semidirect |
| 3. #19099198 | C2 | semidirect |
| 4. #19098813 | C2 | semidirect |
| 5. #19098760 | C2 | semidirect |
| 6. #19098755 | C2 | semidirect |
| 7. #19098705 | C2 | semidirect |
| 8. #19098695 | C2 | semidirect |
| 9. C4×#11929613 | C2 | semidirect |
| 10. #19098642 | C2 | semidirect |
| 11. #493×C79 | C2 | semidirect |
| 12. C2×#11929623 | C22 | semidirect |
| 17. C2×#11929612 | C22 | semidirect |
| 19. C2×#11929607 | C22 | semidirect |
| 24. #14579132 | C22 | semidirect |
| 26. C4×Dic158 | C22 | semidirect |
| 30. #14579093 | C22 | semidirect |
| 31. C4⋊(C79⋊C8) | C22 | semidirect |
| 32. #14579086 | C22 | semidirect |
| 34. #14579082 | C22 | semidirect |
| 35. #14579082 | C22 | semidirect |
| 36. (C2×D79)⋊C8 | C22 | semidirect |
| 37. C2×D8×C79 | C22 | semidirect |
| 38. C2×D8×C79 | C22 | semidirect |
| 40. #127×C79 | C22 | semidirect |
| 41. C4×C8×C79 | C22 | semidirect |
| 58. #11929613 | D4 | semidirect |
| 117. Dic158 | C2×D4 | semidirect |
| 119. C8×C79 | C2×D4 | semidirect |
| 136. C4×C79 | AGL(1,ℤ/8) | semidirect |
| 151. C79 | #3274 | semidirect |
| 155. #493 | D79 | semidirect |
| 170. C2×D8 | C2×D79 | semidirect |
| 171. C2×D8 | C2×D79 | semidirect |
| 175. #127 | C2×D79 | semidirect |
| 192. C4×C8 | C2×D79 | semidirect |
| 271. C8 | D4×D79 | semidirect |
| 291. C4 | #14579185 | semidirect |