Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×D3×C16 | C2 | semidirect |
| 3. C3×C22⋊C16 | C2 | semidirect |
| 4. #4549 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 15. C2×C3×C16 | C22 | semidirect |
| 16. C2×C3⋊C16 | C22 | semidirect |
| 22. C22⋊C16 | D3 | direct (N × H) |
| 54. C2×C16 | C2×D3 | semidirect |
| 58. C22×D3 | C16 | semidirect |
| 101. C22×C3 | C2×C16 | semidirect |
| 108. C2×D3 | C2×C16 | semidirect |
| 143. D3 | C22⋊C16 | direct (N × H) |
| 153. C22 | D3×C16 | semidirect |
| 160. C3 | C2×C22⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×D3×C16 | 2 |
| C3×C22⋊C16 | 2 |
| #4549 | 2 |
| (C2×D3)⋊C16 | 2 |
| C2×C22⋊C16 | 3 |