Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #5600 | C2 | semidirect |
| 3. #5155 | C2 | semidirect |
| 4. #5152 | C2 | semidirect |
| 5. #5137 | C2 | semidirect |
| 6. Dic3×M16 | C2 | semidirect |
| 7. #5042 | C2 | semidirect |
| 8. #4858 | C2 | semidirect |
| 9. #4853 | C2 | semidirect |
| 10. #4768 | C2 | semidirect |
| 11. #4757 | C2 | semidirect |
| 214. C3 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5600 | 2 |
| C3×#469 | 2 |
| #5155 | 2 |
| #5152 | 2 |
| #5137 | 2 |
| Dic3×M16 | 2 |
| #5042 | 2 |
| #4858 | 2 |
| #4853 | 2 |
| #4768 | 2 |
| #4757 | 2 |
| #3183 | 3 |