Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 101 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×#823 | C2 | semidirect |
| 4. #4924 | C2 | semidirect |
| 21. C4×M16 | D3 | semidirect |
| 33. C3×M16 | D4 | semidirect |
| 82. M16 | D12 | semidirect |
| 95. C3×C4 | #100 | semidirect |
| 128. C4 | #823 | semidirect |
| 132. C3 | #1965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C3×C4×M16 | 2 |
| C2×#823 | 2 |
| #4924 | 2 |
| #1965 | 3 |