Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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. #4527 | C2 | semidirect |
| 7. C3×#117 | C4 | semidirect |
| 8. C2×C3×C22⋊C4 | C4 | semidirect |
| 32. #117 | Dic3 | semidirect |
| 34. C2×C22⋊C4 | Dic3 | semidirect |
| 111. C3 | #1828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#518 | 2 |
| C2×#834 | 2 |
| #4527 | 2 |
| #1828 | 3 |