Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5578 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5173 | C2 | semidirect |
| 5. #5167 | C2 | semidirect |
| 6. #5075 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 10. #4783 | C2 | semidirect |
| 11. #4765 | C2 | semidirect |
| 51. #460 | D3 | semidirect |
| 275. C3 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5716 | 2 |
| #5578 | 2 |
| C3×#460 | 2 |
| #5173 | 2 |
| #5167 | 2 |
| #5075 | 2 |
| #5031 | 2 |
| #4849 | 2 |
| #4835 | 2 |
| #4783 | 2 |
| #4765 | 2 |
| #3216 | 3 |