Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×D3×C8 | C2 | semidirect |
| 3. C2×#892 | C2 | semidirect |
| 4. C2×C3×#103 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4804 | C2 | direct (N × H) |
| 13. C2×#239 | C4 | semidirect |
| 26. C2×D3×C8 | C22 | semidirect |
| 28. #892 | C22 | semidirect |
| 29. C3×#103 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #809 | C22 | semidirect |
| 38. C2×#103 | D3 | semidirect |
| 54. #239 | C2×C4 | semidirect |
| 98. #103 | C2×D3 | semidirect |
| 225. C2×C3 | #416 | semidirect |
| 250. C3 | C2×#416 | semidirect |
| 253. C2 | #4804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C22×D3×C8 | 2 |
| C2×#892 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| C2×#821 | 2 |
| C2×#809 | 2 |
| #4804 | 2 |
| C2×#416 | 3 |