Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 3. #5124 | C2 | semidirect |
| 5. C3×#344 | C2 | semidirect |
| 6. #4559 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 25. #344 | D3 | semidirect |
| 165. C3 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5131 | 2 |
| C2×#823 | 2 |
| #5124 | 2 |
| #5001 | 2 |
| C3×#344 | 2 |
| #4559 | 2 |
| #4531 | 2 |
| #2081 | 3 |