Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5470 | C2 | semidirect |
| 3. C3×C4×M16 | C2 | semidirect |
| 4. #5137 | C2 | semidirect |
| 6. #4715 | C2 | semidirect |
| 7. #4714 | C2 | semidirect |
| 8. #4703 | C2 | semidirect |
| 9. #4702 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 54. C4×M16 | D3 | semidirect |
| 253. C3 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| #5470 | 2 |
| C3×C4×M16 | 2 |
| #5137 | 2 |
| #5134 | 2 |
| #4715 | 2 |
| #4714 | 2 |
| #4703 | 2 |
| #4702 | 2 |
| C4×Dic12 | 2 |
| C4×#204 | 2 |
| #3172 | 3 |