Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5769 | C2 | semidirect |
| 2. #5766 | C2 | semidirect |
| 3. C3×#510 | C2 | semidirect |
| 4. #5194 | C2 | semidirect |
| 5. C2×#828 | C2 | semidirect |
| 6. #4919 | C2 | semidirect |
| 7. #4918 | C2 | semidirect |
| 8. #4914 | C2 | semidirect |
| 9. D3×SD32 | C2 | semidirect |
| 10. #4908 | C2 | semidirect |
| 11. #4907 | C2 | semidirect |
| 16. C2×C3×Q16 | C22 | semidirect |
| 20. #919 | C22 | semidirect |
| 22. D3×Q16 | C22 | semidirect |
| 25. #904 | C22 | semidirect |
| 28. C3×Q32 | C22 | semidirect |
| 29. C3×SD32 | C22 | semidirect |
| 30. C3×M32 | C22 | semidirect |
| 31. #829 | C22 | semidirect |
| 32. #828 | C22 | semidirect |
| 33. #828 | C22 | semidirect |
| 34. #828 | C22 | semidirect |
| 35. #827 | C22 | semidirect |
| 36. #826 | C22 | semidirect |
| 37. C2×C3⋊C16 | C22 | semidirect |
| 38. #800 | C22 | semidirect |
| 39. D48 | C22 | semidirect |
| 40. #798 | C22 | semidirect |
| 41. D3×C16 | C22 | semidirect |
| 45. #510 | D3 | semidirect |
| 100. C2×Q16 | C2×D3 | semidirect |
| 105. Q32 | C2×D3 | semidirect |
| 111. SD32 | C2×D3 | semidirect |
| 115. M32 | C2×D3 | semidirect |
| 246. C3 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5769 | 2 |
| #5766 | 2 |
| C3×#510 | 2 |
| #5194 | 2 |
| C2×#828 | 2 |
| #4919 | 2 |
| #4918 | 2 |
| #4914 | 2 |
| D3×SD32 | 2 |
| #4908 | 2 |
| #4907 | 2 |
| #3416 | 3 |