Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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×#890 | C2 | semidirect |
| 3. C3×#480 | C2 | semidirect |
| 4. #5034 | C2 | semidirect |
| 5. #4967 | C2 | semidirect |
| 6. #4891 | C2 | semidirect |
| 7. #4876 | C2 | semidirect |
| 8. #4764 | C2 | semidirect |
| 9. #4763 | C2 | semidirect |
| 10. #4735 | C2 | semidirect |
| 11. #4719 | C2 | semidirect |
| 51. #480 | D3 | semidirect |
| 262. C3 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5596 | 2 |
| C2×#890 | 2 |
| C3×#480 | 2 |
| #5034 | 2 |
| #4967 | 2 |
| #4891 | 2 |
| #4876 | 2 |
| #4764 | 2 |
| #4763 | 2 |
| #4735 | 2 |
| #4719 | 2 |
| #3234 | 3 |