Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5542 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5114 | C2 | semidirect |
| 5. #5113 | C2 | semidirect |
| 6. #4851 | C2 | semidirect |
| 7. #4848 | C2 | semidirect |
| 8. #4737 | C2 | semidirect |
| 9. #4733 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. #4694 | C2 | semidirect |
| 51. C8×D4 | D3 | semidirect |
| 249. C3 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5553 | 2 |
| #5542 | 2 |
| C3×C8×D4 | 2 |
| #5114 | 2 |
| #5113 | 2 |
| #4851 | 2 |
| #4848 | 2 |
| #4737 | 2 |
| #4733 | 2 |
| C4×Dic12 | 2 |
| #4694 | 2 |
| #3304 | 3 |