Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5624 | C2 | semidirect |
| 2. C3×#467 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. Dic3×Q16 | C2 | semidirect |
| 6. C2×C8×Dic3 | C2 | semidirect |
| 7. #5048 | C2 | semidirect |
| 8. #4878 | C2 | semidirect |
| 9. #4872 | C2 | semidirect |
| 10. #4800 | C2 | semidirect |
| 11. #4788 | C2 | semidirect |
| 44. #467 | D3 | semidirect |
| 231. C3 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5624 | 2 |
| C3×#467 | 2 |
| #5191 | 2 |
| Dic3×Q16 | 2 |
| #5115 | 2 |
| C2×C8×Dic3 | 2 |
| #5048 | 2 |
| #4878 | 2 |
| #4872 | 2 |
| #4800 | 2 |
| #4788 | 2 |
| #3168 | 3 |