Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×C3×Q16 | C2 | semidirect |
| 3. C2×#946 | C2 | semidirect |
| 4. C22×#215 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. #5187 | C2 | direct (N × H) |
| 7. C2×#821 | C2 | semidirect |
| 8. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 21. C2×C3×Q16 | C22 | semidirect |
| 24. #946 | C22 | semidirect |
| 26. C2×#215 | C22 | semidirect |
| 31. #835 | C22 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. (C2×D3)⋊C8 | C22 | semidirect |
| 35. C22×Q16 | D3 | semidirect |
| 93. C2×Q16 | C2×D3 | semidirect |
| 239. C2×C3 | #452 | semidirect |
| 264. C3 | C2×#452 | semidirect |
| 267. C2 | #5187 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C22×C3×Q16 | 2 |
| C2×#946 | 2 |
| C22×#215 | 2 |
| C2×#835 | 2 |
| #5187 | 2 |
| C2×#821 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#452 | 3 |