Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
270 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×M16 | C2 | semidirect |
| 3. C4×#208 | C2 | semidirect |
| 4. #4464 | C2 | semidirect |
| 23. C4×M16 | D3 | semidirect |
| 157. C3 | #1525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C3×C4×M16 | 2 |
| C4×#208 | 2 |
| #4464 | 2 |
| #1525 | 3 |