Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 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. C2×#944 | C2 | semidirect |
| 3. C3×#448 | C2 | semidirect |
| 4. #5227 | C2 | semidirect |
| 5. #5175 | C2 | semidirect |
| 6. #5162 | C2 | semidirect |
| 7. #5040 | C2 | semidirect |
| 8. #4818 | C2 | semidirect |
| 9. #4792 | C2 | semidirect |
| 10. #4738 | C2 | semidirect |
| 11. #4718 | C2 | semidirect |
| 53. #448 | D3 | semidirect |
| 150. C2×Dic3 | SD16 | semidirect |
| 286. C3 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#944 | 2 |
| #5596 | 2 |
| C3×#448 | 2 |
| #5227 | 2 |
| #5175 | 2 |
| #5162 | 2 |
| #5040 | 2 |
| #4818 | 2 |
| #4792 | 2 |
| #4738 | 2 |
| #4718 | 2 |
| #3206 | 3 |