Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5539 | C2 | semidirect |
| 4. #5009 | C2 | semidirect |
| 5. #4876 | C2 | semidirect |
| 6. #4766 | C2 | semidirect |
| 7. #4759 | C2 | semidirect |
| 8. #4683 | C2 | semidirect |
| 9. #4679 | C2 | semidirect |
| 51. C3×D8 | Q8 | semidirect |
| 120. D8 | Dic6 | semidirect |
| 188. C3 | #3389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5539 | 2 |
| C3×C4×D8 | 2 |
| #5152 | 2 |
| #5009 | 2 |
| #4876 | 2 |
| #4766 | 2 |
| #4759 | 2 |
| #4683 | 2 |
| #4679 | 2 |
| #3389 | 3 |