Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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×C3×#104 | C2 | semidirect |
| 3. #5232 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #4939 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 30. C2×#104 | D3 | semidirect |
| 56. C3×M16 | D4 | semidirect |
| 151. M16 | #67 | semidirect |
| 253. C3 | #2037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5830 | 2 |
| C2×C3×#104 | 2 |
| #5232 | 2 |
| C2×#823 | 2 |
| #5121 | 2 |
| #4939 | 2 |
| #4523 | 2 |
| #2037 | 3 |