Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. C2×C3×#103 | C2 | semidirect |
| 4. C2×#835 | C2 | semidirect |
| 6. C2×#818 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4811 | C2 | direct (N × H) |
| 25. C3×#103 | C22 | semidirect |
| 26. #835 | C22 | semidirect |
| 28. #818 | C22 | semidirect |
| 29. #807 | C22 | semidirect |
| 36. C2×#103 | D3 | semidirect |
| 86. #103 | C2×D3 | semidirect |
| 190. C2×C3 | #484 | semidirect |
| 211. C3 | C2×#484 | semidirect |
| 213. C2 | #4811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#946 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#818 | 2 |
| C2×#807 | 2 |
| #4811 | 2 |
| C2×#484 | 3 |