Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. C2×#890 | C2 | semidirect |
| 3. C2×C3×#106 | C2 | semidirect |
| 5. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4871 | C2 | direct (N × H) |
| 24. #890 | C22 | semidirect |
| 25. C3×#106 | C22 | semidirect |
| 27. Dic3⋊C8 | C22 | semidirect |
| 29. #807 | C22 | semidirect |
| 34. C2×#106 | D3 | semidirect |
| 82. #106 | C2×D3 | semidirect |
| 180. C2×C3 | #478 | semidirect |
| 201. C3 | C2×#478 | semidirect |
| 203. C2 | #4871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×#890 | 2 |
| C2×C3×#106 | 2 |
| C2×#821 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#809 | 2 |
| C2×#807 | 2 |
| #4871 | 2 |
| C2×#478 | 3 |