Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C3×#335 | C2 | semidirect |
| 4. #4480 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 21. #335 | D3 | semidirect |
| 37. D3×C8 | C8 | semidirect |
| 128. C3 | #1564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4833 | 2 |
| C4×D3×C8 | 2 |
| C3×#335 | 2 |
| #4480 | 2 |
| #4458 | 2 |
| #1564 | 3 |