Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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. #5237 | C2 | semidirect |
| 4. #5132 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 6. #4924 | C2 | semidirect |
| 7. C3⋊#338 | C2 | semidirect |
| 33. C2×#104 | D3 | semidirect |
| 238. C3 | #2050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5822 | 2 |
| C2×C3×#104 | 2 |
| #5237 | 2 |
| #5132 | 2 |
| C2×#805 | 2 |
| #4924 | 2 |
| C3⋊#338 | 2 |
| #2050 | 3 |