Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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 | direct (N × H) |
| 9. C3×M32 | C4 | semidirect |
| 11. C2×C3×C16 | C4 | semidirect |
| 33. C3×C16 | C2×C4 | semidirect |
| 37. M32 | Dic3 | semidirect |
| 39. C2×C16 | Dic3 | semidirect |
| 71. C16 | C2×Dic3 | semidirect |
| 97. C2×C3 | #365 | semidirect |
| 108. C3 | C2×#365 | semidirect |
| 111. C2 | #4513 | direct (N × H) |
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 |
| C2×#817 | 2 |
| #4513 | 2 |
| C2×#365 | 3 |