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. D3×C4⋊Q8 | C2 | semidirect |
| 3. C3×#461 | C2 | semidirect |
| 4. #5175 | C2 | semidirect |
| 5. #5170 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5019 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 10. #4806 | C2 | semidirect |
| 11. #4792 | C2 | semidirect |
| 51. #461 | D3 | semidirect |
| 157. C4×D3 | SD16 | semidirect |
| 290. C3 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5548 | 2 |
| C3×#461 | 2 |
| #5175 | 2 |
| #5170 | 2 |
| #5083 | 2 |
| #5019 | 2 |
| #4841 | 2 |
| #4833 | 2 |
| #4806 | 2 |
| #4792 | 2 |
| #3206 | 3 |