Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×D3×Q16 | C2 | semidirect |
| 3. C2×C3×Q32 | C2 | semidirect |
| 4. C2×#829 | C2 | semidirect |
| 5. C2×#828 | C2 | semidirect |
| 6. #4918 | C2 | direct (N × H) |
| 7. C2×#800 | C2 | semidirect |
| 8. C2×#798 | C2 | semidirect |
| 19. D3×Q16 | C22 | semidirect |
| 23. C3×Q32 | C22 | semidirect |
| 25. #829 | C22 | semidirect |
| 26. #828 | C22 | semidirect |
| 28. #800 | C22 | semidirect |
| 29. #798 | C22 | semidirect |
| 34. C2×Q32 | D3 | semidirect |
| 81. Q32 | C2×D3 | semidirect |
| 175. C2×C3 | #510 | semidirect |
| 190. C3 | C2×#510 | semidirect |
| 193. C2 | #4918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×D3×Q16 | 2 |
| C2×C3×Q32 | 2 |
| C2×#829 | 2 |
| C2×#828 | 2 |
| #4918 | 2 |
| C2×#800 | 2 |
| C2×#798 | 2 |
| C2×#510 | 3 |