Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×#216 | C2 | semidirect |
| 3. C22×#214 | C2 | semidirect |
| 4. C2×#924 | C2 | semidirect |
| 5. #5239 | C2 | direct (N × H) |
| 6. C2×#835 | C2 | semidirect |
| 7. C2×#832 | C2 | semidirect |
| 8. C2×#830 | C2 | semidirect |
| 22. C2×#216 | C22 | semidirect |
| 24. C2×#214 | C22 | semidirect |
| 27. #924 | C22 | semidirect |
| 31. #835 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 33. #830 | C22 | semidirect |
| 241. C2×C3 | #452 | semidirect |
| 264. C3 | C2×#452 | semidirect |
| 267. C2 | #5239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C22×#216 | 2 |
| C22×#214 | 2 |
| C2×#924 | 2 |
| #5239 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| C2×#830 | 2 |
| C2×#452 | 3 |