Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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×#487 | C2 | semidirect |
| 3. #5091 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 27. #487 | D3 | semidirect |
| 176. C3 | #1637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| C3×#487 | 2 |
| #5091 | 2 |
| #5084 | 2 |
| #4547 | 2 |
| #4459 | 2 |
| #4456 | 2 |
| #1637 | 3 |