Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 145 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. D3×C4⋊Q8 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. #5070 | C2 | semidirect |
| 6. D3×#102 | C2 | semidirect |
| 7. #4760 | C2 | semidirect |
| 8. #4694 | C2 | semidirect |
| 9. C4×D3×C8 | C2 | semidirect |
| 15. C3×C4⋊Q8 | C22 | semidirect |
| 25. #888 | C22 | semidirect |
| 28. #869 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. C3×C4×C8 | C22 | semidirect |
| 31. #832 | C22 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. C8×Dic3 | C22 | semidirect |
| 34. #809 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 42. #486 | D3 | direct (N × H) |
| 88. C4⋊Q8 | C2×D3 | semidirect |
| 100. #102 | C2×D3 | semidirect |
| 103. C4×C8 | C2×D3 | semidirect |
| 226. D3 | #486 | direct (N × H) |
| 246. C3 | C2×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| D3×#127 | 2 |
| C3×#486 | 2 |
| #5088 | 2 |
| #5070 | 2 |
| D3×#102 | 2 |
| #4760 | 2 |
| #4694 | 2 |
| C4×D3×C8 | 2 |
| C2×#486 | 3 |