Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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. #5079 | C2 | semidirect |
| 3. #4849 | C2 | semidirect |
| 5. C3×#333 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 30. #333 | D3 | semidirect |
| 84. D12 | Q16 | semidirect |
| 172. C3 | #1644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5079 | 2 |
| #4849 | 2 |
| #4846 | 2 |
| C3×#333 | 2 |
| #4484 | 2 |
| #4483 | 2 |
| #1644 | 3 |