Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5155 | C2 | semidirect |
| 3. #5151 | C2 | semidirect |
| 4. C2×#827 | C2 | semidirect |
| 5. C2×#826 | C2 | semidirect |
| 6. C2×#800 | C2 | semidirect |
| 7. #4502 | C2 | semidirect |
| 27. C2×D16 | D3 | semidirect |
| 50. C3×C16 | D4 | semidirect |
| 51. C3⋊C16 | D4 | semidirect |
| 105. C16 | #67 | semidirect |
| 151. C3 | #2250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| #5155 | 2 |
| #5151 | 2 |
| C2×#827 | 2 |
| C2×#826 | 2 |
| C2×#800 | 2 |
| #4502 | 2 |
| #2250 | 3 |