Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. #5585 | C2 | semidirect |
| 2. Q8×D12 | C2 | semidirect |
| 3. C3×#446 | C2 | semidirect |
| 4. #4851 | C2 | semidirect |
| 5. #4844 | C2 | semidirect |
| 7. #4842 | C2 | semidirect |
| 8. #4714 | C2 | semidirect |
| 9. #4711 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 50. #446 | D3 | semidirect |
| 243. C3 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| Q8×D12 | 2 |
| C3×#446 | 2 |
| #4851 | 2 |
| #4844 | 2 |
| #4843 | 2 |
| #4842 | 2 |
| #4714 | 2 |
| #4711 | 2 |
| #4694 | 2 |
| C4×#204 | 2 |
| #3373 | 3 |