Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
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. #16813668 | C2 | semidirect |
| 2. #16813667 | C2 | semidirect |
| 3. #16813650 | C2 | semidirect |
| 4. #16813649 | C2 | semidirect |
| 5. #16813646 | C2 | semidirect |
| 6. #16813643 | C2 | semidirect |
| 7. #16813642 | C2 | semidirect |
| 8. C2×#14268632 | C2 | semidirect |
| 9. D8×D113 | C2 | semidirect |
| 10. #16813630 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 12. #14268648 | C22 | semidirect |
| 15. #14268647 | C22 | semidirect |
| 17. #14268646 | C22 | semidirect |
| 19. C2×D452 | C22 | semidirect |
| 23. D4×D113 | C22 | semidirect |
| 24. D4×D113 | C22 | semidirect |
| 25. #14268637 | C22 | semidirect |
| 26. #14268636 | C22 | semidirect |
| 27. #14268635 | C22 | semidirect |
| 28. #14268634 | C22 | semidirect |
| 29. D904 | C22 | semidirect |
| 30. #14268632 | C22 | semidirect |
| 31. #14268632 | C22 | semidirect |
| 32. #14268632 | C22 | semidirect |
| 33. #14268630 | C22 | semidirect |
| 34. C2×#11744751 | C22 | semidirect |
| 35. C8×D113 | C22 | semidirect |
| 36. #41×C113 | C22 | semidirect |
| 37. C2×D4×C113 | C22 | semidirect |
| 38. SD16×C113 | C22 | semidirect |
| 39. D8×C113 | C22 | semidirect |
| 40. M16×C113 | C22 | semidirect |
| 93. C113 | #576 | semidirect |
| 100. AGL(1,ℤ/8) | D113 | semidirect |
| 112. #41 | C2×D113 | semidirect |
| 120. C2×D4 | C2×D113 | semidirect |
| 125. SD16 | C2×D113 | semidirect |
| 130. D8 | C2×D113 | semidirect |
| 132. M16 | C2×D113 | semidirect |