Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. C2×C3×D16 | C2 | semidirect |
| 2. #5151 | C2 | semidirect |
| 3. Dic3×D8 | C2 | semidirect |
| 4. C2×#826 | C2 | semidirect |
| 5. #4562 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. Dic3⋊C16 | C2 | semidirect |
| 23. C2×D16 | D3 | semidirect |
| 38. C3×D8 | D4 | semidirect |
| 93. D8 | #67 | semidirect |
| 115. Dic3 | D16 | semidirect |
| 156. C3 | #2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| #5151 | 2 |
| Dic3×D8 | 2 |
| C2×#826 | 2 |
| #4562 | 2 |
| #4509 | 2 |
| Dic3⋊C16 | 2 |
| #2206 | 3 |