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. #5680 | C2 | semidirect |
| 2. C3×#495 | C2 | semidirect |
| 3. #5188 | C2 | semidirect |
| 4. Dic3×Q16 | C2 | semidirect |
| 5. #5171 | C2 | semidirect |
| 6. Dic3×SD16 | C2 | semidirect |
| 8. Dic3×D8 | C2 | semidirect |
| 9. #5056 | C2 | semidirect |
| 10. C4×D3×C8 | C2 | semidirect |
| 11. #4683 | C2 | semidirect |
| 42. #495 | 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 |
|---|---|
| #5680 | 2 |
| C3×#495 | 2 |
| #5188 | 2 |
| Dic3×Q16 | 2 |
| #5171 | 2 |
| Dic3×SD16 | 2 |
| #5157 | 2 |
| Dic3×D8 | 2 |
| #5056 | 2 |
| C4×D3×C8 | 2 |
| #4683 | 2 |
| #3168 | 3 |