Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 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×SD16×D79 | C2 | semidirect |
| 2. Q8×D316 | C2 | semidirect |
| 4. #19098936 | C2 | semidirect |
| 5. #19098793 | C2 | semidirect |
| 6. #19098768 | C2 | semidirect |
| 7. #19098763 | C2 | semidirect |
| 8. #19098715 | C2 | semidirect |
| 9. #19098703 | C2 | semidirect |
| 10. C8×D316 | C2 | semidirect |
| 11. C4×SD16×C79 | C2 | semidirect |
| 12. C2×Q8×D79 | C22 | semidirect |
| 15. C2×#11929613 | C22 | semidirect |
| 16. C2×#11929613 | C22 | semidirect |
| 18. C2×#11929611 | C22 | semidirect |
| 20. C2×C8×D79 | C22 | semidirect |
| 22. #14579161 | C22 | semidirect |
| 25. #14579141 | C22 | semidirect |
| 31. C4⋊(C79⋊C8) | C22 | semidirect |
| 32. #14579084 | 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 |
| 90. Q8×C79 | C2×D4 | semidirect |
| 108. D316 | SD16 | direct (N × H) |
| 116. C8×C79 | C2×D4 | semidirect |
| 128. C2×D79 | C2×SD16 | semidirect |
| 133. C4×C79 | C2×SD16 | semidirect |
| 145. C79 | D4×SD16 | semidirect |
| 155. C4×SD16 | D79 | semidirect |
| 175. C4×Q8 | C2×D79 | semidirect |
| 179. #106 | C2×D79 | semidirect |
| 182. #103 | C2×D79 | semidirect |
| 186. C4×C8 | C2×D79 | semidirect |
| 210. SD16 | D316 | direct (N × H) |
| 238. Q8 | C2×D316 | semidirect |
| 262. C8 | C2×D316 | semidirect |
| 280. C4 | SD16×D79 | semidirect |