Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C3×#462 | C2 | semidirect |
| 5. #5182 | C2 | semidirect |
| 6. #5090 | C2 | semidirect |
| 7. #5021 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 11. #4793 | C2 | semidirect |
| 53. #462 | D3 | semidirect |
| 144. C4×D3 | Q16 | semidirect |
| 254. C3 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5578 | 2 |
| C3×#462 | 2 |
| #5188 | 2 |
| #5182 | 2 |
| #5090 | 2 |
| #5021 | 2 |
| #4850 | 2 |
| D3×C4⋊C8 | 2 |
| #4813 | 2 |
| #4793 | 2 |
| #3249 | 3 |