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×#14579188 | C2 | semidirect |
| 2. #19099235 | C2 | semidirect |
| 3. D4×D316 | C2 | semidirect |
| 4. #19098940 | C2 | semidirect |
| 5. #19098817 | C2 | semidirect |
| 6. #19098763 | C2 | semidirect |
| 7. #19098758 | C2 | semidirect |
| 8. #19098711 | C2 | semidirect |
| 9. #19098698 | C2 | semidirect |
| 10. #19098642 | C2 | semidirect |
| 11. C4×SD16×C79 | C2 | semidirect |
| 12. C2×#11929625 | C22 | semidirect |
| 16. C2×#11929611 | C22 | semidirect |
| 17. C2×D632 | C22 | semidirect |
| 18. C2×D632 | C22 | semidirect |
| 20. C2×#11929607 | C22 | semidirect |
| 23. #14579158 | C22 | semidirect |
| 26. #14579136 | C22 | semidirect |
| 31. C4⋊(C79⋊C8) | C22 | semidirect |
| 32. #14579081 | C22 | semidirect |
| 33. #14579081 | C22 | semidirect |
| 34. (C2×D79)⋊C8 | C22 | semidirect |
| 36. C4×Q8×C79 | C22 | semidirect |
| 38. #106×C79 | C22 | semidirect |
| 39. #103×C79 | C22 | semidirect |
| 41. C4×C8×C79 | C22 | semidirect |
| 74. SD16×C79 | D4 | semidirect |
| 91. Q8×C79 | C2×D4 | semidirect |
| 119. C8×C79 | C2×D4 | semidirect |
| 139. C4×C79 | AGL(1,ℤ/8) | semidirect |
| 151. C79 | #3274 | semidirect |
| 161. C4×SD16 | D79 | semidirect |
| 181. C4×Q8 | C2×D79 | semidirect |
| 185. #106 | C2×D79 | semidirect |
| 187. #103 | C2×D79 | semidirect |
| 192. C4×C8 | C2×D79 | semidirect |
| 216. SD16 | D316 | semidirect |
| 242. Q8 | C2×D316 | semidirect |
| 271. C8 | C2×D316 | semidirect |
| 291. C4 | #14579188 | semidirect |