Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×#443 | C2 | semidirect |
| 3. #4700 | C2 | semidirect |
| 4. #4567 | C2 | semidirect |
| 5. #4497 | C2 | semidirect |
| 6. #4493 | C2 | semidirect |
| 7. C4×C3⋊C16 | C2 | semidirect |
| 16. #829 | C4 | semidirect |
| 17. #828 | C4 | semidirect |
| 18. #827 | C4 | semidirect |
| 19. #826 | C4 | semidirect |
| 26. #443 | D3 | semidirect |
| 138. C3 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#443 | 2 |
| #5194 | 2 |
| #4700 | 2 |
| #4567 | 2 |
| #4497 | 2 |
| #4493 | 2 |
| C4×C3⋊C16 | 2 |
| #2178 | 3 |