Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 8. #4878 | C2 | semidirect |
| 9. #4876 | C2 | semidirect |
| 10. #4858 | C2 | semidirect |
| 11. #4856 | C2 | semidirect |
| 62. C3×M16 | Q8 | semidirect |
| 90. #208 | Q8 | semidirect |
| 154. M16 | Dic6 | semidirect |
| 244. C3 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| C2×#890 | 2 |
| C3×#428 | 2 |
| #5121 | 2 |
| Dic3×M16 | 2 |
| #4995 | 2 |
| #4964 | 2 |
| #4878 | 2 |
| #4876 | 2 |
| #4858 | 2 |
| #4856 | 2 |
| #3166 | 3 |