Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. C3×#475 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4855 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 11. #4792 | C2 | semidirect |
| 53. #475 | D3 | semidirect |
| 252. C3 | #3229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5578 | 2 |
| C3×#475 | 2 |
| #5094 | 2 |
| #5020 | 2 |
| #4862 | 2 |
| #4855 | 2 |
| #4851 | 2 |
| #4833 | 2 |
| #4805 | 2 |
| #4792 | 2 |
| #3229 | 3 |