Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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. #4873 | C2 | semidirect |
| 4. C3×#366 | C2 | semidirect |
| 5. #4502 | C2 | semidirect |
| 6. #4492 | C2 | semidirect |
| 20. #800 | C4 | semidirect |
| 24. #366 | D3 | semidirect |
| 40. Dic12 | C2×C4 | semidirect |
| 43. C3×C16 | C2×C4 | semidirect |
| 88. C16 | C4×D3 | semidirect |
| 130. C3 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#800 | 2 |
| #4873 | 2 |
| #4872 | 2 |
| C3×#366 | 2 |
| #4502 | 2 |
| #4492 | 2 |
| #4491 | 2 |
| #2175 | 3 |