Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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. #4512 | C2 | semidirect |
| 9. C3×M32 | C4 | semidirect |
| 11. C2×C3×C16 | C4 | semidirect |
| 14. #812 | C4 | semidirect |
| 16. C2×C3⋊C16 | C4 | semidirect |
| 41. M32 | Dic3 | semidirect |
| 44. C2×C16 | Dic3 | semidirect |
| 110. C3 | #2110 | 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 |
| C2×#812 | 2 |
| #4512 | 2 |
| #2110 | 3 |