Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#951 | C2 | semidirect |
| 3. C2×#901 | C2 | semidirect |
| 4. #5526 | C2 | semidirect |
| 5. C3×#416 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. #4995 | C2 | semidirect |
| 8. #4816 | C2 | semidirect |
| 9. #4813 | C2 | semidirect |
| 10. #4780 | C2 | semidirect |
| 11. #4778 | C2 | semidirect |
| 53. #416 | D3 | semidirect |
| 93. #208 | D4 | semidirect |
| 280. C3 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5833 | 2 |
| C2×#951 | 2 |
| C2×#901 | 2 |
| #5526 | 2 |
| C3×#416 | 2 |
| C2×#816 | 2 |
| #4995 | 2 |
| #4816 | 2 |
| #4813 | 2 |
| #4780 | 2 |
| #4778 | 2 |
| #3063 | 3 |