Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 123 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×#477 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 5. C4×#216 | C2 | semidirect |
| 6. #4884 | C2 | semidirect |
| 7. D3×#107 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 10. #4813 | C2 | semidirect |
| 11. #4811 | C2 | semidirect |
| 48. #477 | D3 | semidirect |
| 128. D12 | Q16 | semidirect |
| 230. C3 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5579 | 2 |
| C3×#477 | 2 |
| #5078 | 2 |
| C4×#216 | 2 |
| #4884 | 2 |
| D3×#107 | 2 |
| #4850 | 2 |
| #4834 | 2 |
| #4813 | 2 |
| #4811 | 2 |
| #3338 | 3 |