Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#204 | C2 | semidirect |
| 3. C2×#875 | C2 | semidirect |
| 4. C2×C4×D12 | C2 | semidirect |
| 5. C2×C3×C4⋊C8 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#816 | C2 | semidirect |
| 8. #4844 | C2 | direct (N × H) |
| 24. C2×#204 | C22 | semidirect |
| 26. #875 | C22 | semidirect |
| 28. C4×D12 | C22 | semidirect |
| 29. C3×C4⋊C8 | C22 | semidirect |
| 30. #821 | C22 | semidirect |
| 31. #816 | C22 | semidirect |
| 37. C2×C4⋊C8 | D3 | semidirect |
| 93. C4⋊C8 | C2×D3 | semidirect |
| 215. C2×C3 | #463 | semidirect |
| 240. C3 | C2×#463 | semidirect |
| 243. C2 | #4844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C22×#204 | 2 |
| C2×#875 | 2 |
| C2×C4×D12 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4844 | 2 |
| C2×#463 | 3 |