Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 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. #4835 | C2 | semidirect |
| 3. #4833 | C2 | semidirect |
| 4. C3×#332 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4485 | C2 | semidirect |
| 30. #332 | D3 | semidirect |
| 187. C3 | #1553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5725 | 2 |
| #4835 | 2 |
| #4833 | 2 |
| C3×#332 | 2 |
| #4547 | 2 |
| #4485 | 2 |
| #1553 | 3 |