Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3×#500 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 5. #5080 | C2 | semidirect |
| 7. #4877 | C2 | semidirect |
| 9. #4681 | C2 | semidirect |
| 38. #500 | D3 | semidirect |
| 200. C3 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C3×#500 | 2 |
| #5093 | 2 |
| #5080 | 2 |
| #4888 | 2 |
| #4877 | 2 |
| #4685 | 2 |
| #4681 | 2 |
| #3231 | 3 |