Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 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×#335 | C2 | semidirect |
| 5. #4480 | C2 | semidirect |
| 6. #4480 | C2 | semidirect |
| 7. #4458 | C2 | semidirect |
| 28. #335 | D3 | semidirect |
| 144. C3 | #1572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4835 | 2 |
| #4833 | 2 |
| #4685 | 2 |
| C3×#335 | 2 |
| #4480 | 2 |
| #4458 | 2 |
| #1572 | 3 |