Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. C3×#529 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. #5067 | C2 | semidirect |
| 4. #5064 | C2 | semidirect |
| 5. #5058 | C2 | semidirect |
| 6. #5055 | C2 | semidirect |
| 7. #5049 | C2 | semidirect |
| 8. #5039 | C2 | semidirect |
| 9. C4×#215 | C2 | semidirect |
| 10. C4×#213 | C2 | semidirect |
| 11. C4×#208 | C2 | semidirect |
| 45. #529 | D3 | semidirect |
| 153. C3⋊C8 | #41 | semidirect |
| 268. C3 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#529 | 2 |
| #5477 | 2 |
| #5067 | 2 |
| #5064 | 2 |
| #5058 | 2 |
| #5055 | 2 |
| #5049 | 2 |
| #5039 | 2 |
| C4×#215 | 2 |
| C4×#213 | 2 |
| C4×#208 | 2 |
| #3171 | 3 |