Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 125 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. #4502 | C2 | semidirect |
| 5. Dic3×C16 | C2 | semidirect |
| 10. C3×M32 | C4 | semidirect |
| 14. C2×C3⋊C16 | C4 | semidirect |
| 38. M32 | Dic3 | semidirect |
| 95. C3 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M32 | 2 |
| #5101 | 2 |
| C22×C3⋊C16 | 2 |
| #4502 | 2 |
| Dic3×C16 | 2 |
| #2108 | 3 |