Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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×#477 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4877 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 11. #4799 | C2 | semidirect |
| 49. #477 | D3 | semidirect |
| 58. D3×Q8 | Q8 | semidirect |
| 256. C3 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×D3×Q8 | 2 |
| C3×#477 | 2 |
| #5091 | 2 |
| #5020 | 2 |
| #4881 | 2 |
| #4877 | 2 |
| #4851 | 2 |
| #4837 | 2 |
| #4802 | 2 |
| #4799 | 2 |
| #3078 | 3 |