Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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. Dic3×D8 | C2 | semidirect |
| 3. #4562 | C2 | semidirect |
| 4. #4504 | C2 | semidirect |
| 5. Dic3×C16 | C2 | semidirect |
| 9. C3×D16 | C4 | semidirect |
| 23. C3×D8 | C2×C4 | semidirect |
| 29. C3×C16 | C2×C4 | semidirect |
| 33. D16 | Dic3 | direct (N × H) |
| 53. D8 | C2×Dic3 | semidirect |
| 60. C16 | C2×Dic3 | semidirect |
| 69. Dic3 | D16 | direct (N × H) |
| 94. C3 | C4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| Dic3×D8 | 2 |
| #4562 | 2 |
| #4504 | 2 |
| Dic3×C16 | 2 |
| C4×D16 | 3 |