Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C22×C3×C16 | C2 | semidirect |
| 3. C22×C3⋊C16 | C2 | semidirect |
| 4. (C2×D3)⋊C16 | C2 | direct (N × H) |
| 14. C2×C3×C16 | C22 | semidirect |
| 16. C2×C3⋊C16 | C22 | semidirect |
| 19. C22×C16 | D3 | semidirect |
| 49. C2×C16 | C2×D3 | semidirect |
| 53. C22×D3 | C16 | semidirect |
| 93. C2×D3 | C2×C16 | semidirect |
| 116. C2×C3 | C22⋊C16 | semidirect |
| 133. C3 | C2×C22⋊C16 | semidirect |
| 135. C2 | (C2×D3)⋊C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C22×C3×C16 | 2 |
| C22×C3⋊C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| C2×C22⋊C16 | 3 |