Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5519 | C2 | semidirect |
| 3. #5233 | C2 | semidirect |
| 4. #5232 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. C2×#832 | C2 | semidirect |
| 7. #5071 | C2 | semidirect |
| 8. #5070 | C2 | semidirect |
| 9. #5056 | C2 | semidirect |
| 10. #5055 | C2 | semidirect |
| 11. #4997 | C2 | semidirect |
| 28. #870 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 31. #835 | C22 | semidirect |
| 32. #835 | C22 | semidirect |
| 37. #832 | C22 | semidirect |
| 38. #832 | C22 | semidirect |
| 39. #832 | C22 | semidirect |
| 40. #803 | C22 | semidirect |
| 41. C4×C3⋊C8 | C22 | semidirect |
| 264. C3 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5519 | 2 |
| #5233 | 2 |
| #5232 | 2 |
| #5215 | 2 |
| C2×#832 | 2 |
| #5071 | 2 |
| #5070 | 2 |
| #5056 | 2 |
| #5055 | 2 |
| #4997 | 2 |
| #3136 | 3 |