Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×C3×Q32 | C2 | semidirect |
| 3. C2×#829 | C2 | semidirect |
| 4. D3×Q32 | C2 | direct (N × H) |
| 5. C2×Dic24 | C2 | semidirect |
| 15. C3×Q32 | C22 | semidirect |
| 17. #829 | C22 | semidirect |
| 19. Dic24 | C22 | semidirect |
| 25. C2×Q32 | D3 | direct (N × H) |
| 54. Q32 | C2×D3 | direct (N × H) |
| 93. C2×D3 | Q32 | direct (N × H) |
| 116. C2×C3 | C2×Q32 | semidirect |
| 118. D3 | C2×Q32 | direct (N × H) |
| 127. C3 | C22×Q32 | semidirect |
| 129. C2 | D3×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C2×C3×Q32 | 2 |
| C2×#829 | 2 |
| D3×Q32 | 2 |
| C2×Dic24 | 2 |
| C2×D3×C16 | 2 |
| C22×Q32 | 3 |