Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 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. C3×#338 | C2 | semidirect |
| 3. C3⋊#338 | C2 | semidirect |
| 14. #338 | D3 | direct (N × H) |
| 93. D3 | #338 | direct (N × H) |
| 104. C3 | C2×#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C3×#338 | 2 |
| C3⋊#338 | 2 |
| C2×#338 | 3 |