Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×D3×Q16 | C2 | semidirect |
| 3. C3×#510 | C2 | semidirect |
| 4. #5195 | C2 | semidirect |
| 5. #5179 | C2 | semidirect |
| 6. #4918 | C2 | semidirect |
| 7. D3×Q32 | C2 | semidirect |
| 8. #4915 | C2 | semidirect |
| 9. D3×SD32 | C2 | semidirect |
| 10. #4909 | C2 | semidirect |
| 11. D3×M32 | C2 | semidirect |
| 16. C2×C3×Q16 | C22 | semidirect |
| 24. D3×Q16 | C22 | semidirect |
| 29. C2×Dic12 | C22 | semidirect |
| 32. C3×Q32 | C22 | semidirect |
| 33. C3×SD32 | C22 | semidirect |
| 34. C3×M32 | C22 | semidirect |
| 35. #829 | C22 | semidirect |
| 36. #829 | C22 | semidirect |
| 37. #828 | C22 | semidirect |
| 38. #827 | C22 | semidirect |
| 39. #812 | C22 | semidirect |
| 40. Dic24 | C22 | semidirect |
| 41. #800 | C22 | semidirect |
| 42. #798 | C22 | semidirect |
| 51. #510 | D3 | direct (N × H) |
| 113. C2×Q16 | C2×D3 | semidirect |
| 120. Q32 | C2×D3 | semidirect |
| 124. SD32 | C2×D3 | semidirect |
| 127. M32 | C2×D3 | semidirect |
| 266. D3 | #510 | direct (N × H) |
| 282. C3 | C2×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#135 | 2 |
| C2×D3×Q16 | 2 |
| C3×#510 | 2 |
| #5195 | 2 |
| #5179 | 2 |
| #4918 | 2 |
| D3×Q32 | 2 |
| #4915 | 2 |
| D3×SD32 | 2 |
| #4909 | 2 |
| D3×M32 | 2 |
| C2×#510 | 3 |