Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 4. C3×#365 | C2 | semidirect |
| 5. #4513 | C2 | semidirect |
| 6. #4494 | C2 | semidirect |
| 7. #4487 | C2 | semidirect |
| 20. #798 | C4 | semidirect |
| 21. D3×C16 | C4 | semidirect |
| 28. #365 | D3 | semidirect |
| 130. C3 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×M32 | 2 |
| D3×#108 | 2 |
| #4860 | 2 |
| C3×#365 | 2 |
| #4513 | 2 |
| #4494 | 2 |
| #4487 | 2 |
| #2155 | 3 |