Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #14579207 | C2 | semidirect |
| 2. #14579206 | C2 | semidirect |
| 3. #14579189 | C2 | semidirect |
| 4. #14579188 | C2 | semidirect |
| 5. #14579185 | C2 | semidirect |
| 6. #14579182 | C2 | semidirect |
| 7. #14579181 | C2 | semidirect |
| 8. C2×#11929609 | C2 | semidirect |
| 9. D8×D79 | C2 | semidirect |
| 10. #14579169 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C79 | C2 | semidirect |
| 12. #11929625 | C22 | semidirect |
| 15. #11929624 | C22 | semidirect |
| 17. #11929623 | C22 | semidirect |
| 19. C2×D316 | C22 | semidirect |
| 23. D4×D79 | C22 | semidirect |
| 24. D4×D79 | C22 | semidirect |
| 25. #11929614 | C22 | semidirect |
| 26. #11929613 | C22 | semidirect |
| 27. #11929612 | C22 | semidirect |
| 28. #11929611 | C22 | semidirect |
| 29. D632 | C22 | semidirect |
| 30. #11929609 | C22 | semidirect |
| 31. #11929609 | C22 | semidirect |
| 32. #11929609 | C22 | semidirect |
| 33. #11929607 | C22 | semidirect |
| 34. C2×C79⋊C8 | C22 | semidirect |
| 35. C8×D79 | C22 | semidirect |
| 36. #41×C79 | C22 | semidirect |
| 37. C2×D4×C79 | C22 | semidirect |
| 38. SD16×C79 | C22 | semidirect |
| 39. D8×C79 | C22 | semidirect |
| 40. M16×C79 | C22 | semidirect |
| 93. C79 | #576 | semidirect |
| 100. AGL(1,ℤ/8) | D79 | semidirect |
| 112. #41 | C2×D79 | semidirect |
| 120. C2×D4 | C2×D79 | semidirect |
| 125. SD16 | C2×D79 | semidirect |
| 130. D8 | C2×D79 | semidirect |
| 132. M16 | C2×D79 | semidirect |