Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. #5075 | C2 | semidirect |
| 3. #4848 | C2 | semidirect |
| 4. #4831 | C2 | semidirect |
| 5. C3×#331 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4480 | C2 | semidirect |
| 30. #331 | D3 | semidirect |
| 89. C3⋊C8 | SD16 | semidirect |
| 167. C3 | #1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5075 | 2 |
| #5073 | 2 |
| #4848 | 2 |
| #4831 | 2 |
| C3×#331 | 2 |
| #4485 | 2 |
| #4480 | 2 |
| #1688 | 3 |