Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 4. C4×#208 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 20. #823 | C4 | direct (N × H) |
| 26. C4×M16 | D3 | semidirect |
| 41. C3×M16 | C2×C4 | semidirect |
| 52. #208 | C2×C4 | semidirect |
| 109. M16 | C4×D3 | semidirect |
| 133. C3×C4 | #100 | semidirect |
| 181. C4 | #823 | direct (N × H) |
| 184. C3 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×C4×M16 | 2 |
| C2×#823 | 2 |
| C4×#208 | 2 |
| #4554 | 2 |
| C4×#100 | 3 |