Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 1. C2×C3×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #5822 | C2 | semidirect |
| 3. #5819 | C2 | semidirect |
| 4. C2×#932 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 6. #5200 | C2 | semidirect |
| 7. #5199 | C2 | semidirect |
| 8. #5132 | C2 | semidirect |
| 9. #5124 | C2 | semidirect |
| 19. #951 | C22 | semidirect |
| 21. #949 | C22 | semidirect |
| 23. #948 | C22 | semidirect |
| 25. C2×#214 | C22 | semidirect |
| 29. C2×#213 | C22 | semidirect |
| 34. #833 | C22 | semidirect |
| 35. #824 | C22 | semidirect |
| 36. #823 | C22 | semidirect |
| 37. #822 | C22 | semidirect |
| 40. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 287. C3 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5822 | 2 |
| #5819 | 2 |
| C2×#932 | 2 |
| C2×#833 | 2 |
| #5200 | 2 |
| #5199 | 2 |
| #5132 | 2 |
| #5124 | 2 |
| #3068 | 3 |