Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Q8×D12 | C2 | semidirect |
| 3. C3×#477 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 5. C4×#215 | C2 | semidirect |
| 6. #4888 | C2 | semidirect |
| 7. #4886 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4806 | C2 | semidirect |
| 11. #4802 | C2 | semidirect |
| 46. #477 | D3 | semidirect |
| 247. C3 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5734 | 2 |
| Q8×D12 | 2 |
| C3×#477 | 2 |
| #5093 | 2 |
| C4×#215 | 2 |
| #4888 | 2 |
| #4886 | 2 |
| #4841 | 2 |
| #4838 | 2 |
| #4806 | 2 |
| #4802 | 2 |
| #3329 | 3 |