Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#926 | C2 | semidirect |
| 3. C2×C3×C22⋊C8 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. C2×#818 | C2 | semidirect |
| 7. C2×#817 | C2 | semidirect |
| 8. #4737 | C2 | direct (N × H) |
| 20. #926 | C22 | semidirect |
| 25. C3×C22⋊C8 | C22 | semidirect |
| 26. #821 | C22 | semidirect |
| 27. #821 | C22 | semidirect |
| 28. #818 | C22 | semidirect |
| 29. #817 | C22 | semidirect |
| 37. C2×C22⋊C8 | D3 | semidirect |
| 87. C22⋊C8 | C2×D3 | semidirect |
| 198. C2×C3 | #482 | semidirect |
| 222. C3 | C2×#482 | semidirect |
| 225. C2 | #4737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×#926 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| C2×#818 | 2 |
| C2×#817 | 2 |
| #4737 | 2 |
| C2×#482 | 3 |