Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 2. C3×C4×M16 | C2 | semidirect |
| 3. C2×#824 | C2 | semidirect |
| 5. #4924 | C2 | semidirect |
| 25. C4×M16 | D3 | semidirect |
| 156. C3 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C3×C4×M16 | 2 |
| C2×#824 | 2 |
| C2×#823 | 2 |
| #4924 | 2 |
| #1967 | 3 |