Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5548 | C2 | semidirect |
| 2. C3×C4×D8 | C2 | semidirect |
| 3. #5157 | C2 | semidirect |
| 4. #5151 | C2 | semidirect |
| 5. C4×#213 | C2 | semidirect |
| 6. #4883 | C2 | semidirect |
| 7. #4874 | C2 | semidirect |
| 8. #4775 | C2 | semidirect |
| 9. #4760 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. C4×D3×C8 | C2 | semidirect |
| 49. C4×D8 | D3 | semidirect |
| 135. C4×D3 | D8 | semidirect |
| 138. C3×C8 | #41 | semidirect |
| 140. C3⋊C8 | #41 | semidirect |
| 222. C8 | #235 | semidirect |
| 248. C3 | #3169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5548 | 2 |
| C3×C4×D8 | 2 |
| #5157 | 2 |
| #5151 | 2 |
| C4×#213 | 2 |
| #4883 | 2 |
| #4874 | 2 |
| #4775 | 2 |
| #4760 | 2 |
| C4×D24 | 2 |
| C4×D3×C8 | 2 |
| #3169 | 3 |