Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5721 | C2 | semidirect |
| 3. C3×#500 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 8. #4876 | C2 | semidirect |
| 9. #4875 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 45. #500 | D3 | semidirect |
| 84. #204 | Q8 | semidirect |
| 134. Dic6 | C2×Q8 | semidirect |
| 136. C3×C8 | C2×Q8 | semidirect |
| 208. C8 | D3×Q8 | semidirect |
| 228. C3 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| #5721 | 2 |
| C3×#500 | 2 |
| #5094 | 2 |
| #5087 | 2 |
| #4891 | 2 |
| #4889 | 2 |
| #4876 | 2 |
| #4875 | 2 |
| C4×#204 | 2 |
| #4679 | 2 |
| #3386 | 3 |