Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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. C3×C22⋊C16 | C2 | semidirect |
| 3. #4549 | C2 | semidirect |
| 14. C22⋊C16 | D3 | semidirect |
| 41. C22×D3 | C16 | semidirect |
| 120. C3 | #1314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D3)⋊C8 | 2 |
| C3×C22⋊C16 | 2 |
| #4549 | 2 |
| #1314 | 3 |