Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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. C3×#416 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5113 | C2 | semidirect |
| 5. #5102 | C2 | semidirect |
| 6. #5006 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 31. #416 | D3 | semidirect |
| 230. C3 | #2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5822 | 2 |
| C3×#416 | 2 |
| #5240 | 2 |
| #5113 | 2 |
| #5102 | 2 |
| #5006 | 2 |
| #4531 | 2 |
| #2053 | 3 |