Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #5728 | C2 | semidirect |
| 3. C3×#476 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5019 | C2 | semidirect |
| 6. #4862 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 11. #4758 | C2 | semidirect |
| 15. C3×C4⋊Q8 | C22 | semidirect |
| 28. #887 | C22 | semidirect |
| 33. #869 | C22 | semidirect |
| 34. C3×#106 | C22 | semidirect |
| 35. C3×C4⋊C8 | C22 | semidirect |
| 38. #816 | C22 | semidirect |
| 39. C8×Dic3 | C22 | semidirect |
| 40. #810 | C22 | semidirect |
| 42. #808 | C22 | semidirect |
| 43. C4⋊(C3⋊C8) | C22 | semidirect |
| 48. #476 | D3 | semidirect |
| 100. C4⋊Q8 | C2×D3 | semidirect |
| 117. #106 | C2×D3 | semidirect |
| 119. C4⋊C8 | C2×D3 | semidirect |
| 156. C4×D3 | SD16 | semidirect |
| 286. C3 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×D3×D4 | 2 |
| C3×#476 | 2 |
| #5084 | 2 |
| #5019 | 2 |
| #4862 | 2 |
| #4852 | 2 |
| #4841 | 2 |
| #4833 | 2 |
| #4776 | 2 |
| #4758 | 2 |
| #3101 | 3 |