Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 4. #4513 | C2 | semidirect |
| 9. C3×M32 | C4 | semidirect |
| 11. C2×C3×C16 | C4 | semidirect |
| 37. M32 | Dic3 | semidirect |
| 39. C2×C16 | Dic3 | semidirect |
| 106. C3 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M32 | 2 |
| C2×#819 | 2 |
| #5106 | 2 |
| #4513 | 2 |
| #2155 | 3 |