Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#949 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. C22×#213 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 6. #5199 | C2 | direct (N × H) |
| 7. C2×#823 | C2 | semidirect |
| 8. C2×#822 | C2 | semidirect |
| 14. C3×AGL(1,ℤ/8) | C22 | semidirect |
| 19. #949 | C22 | semidirect |
| 21. #948 | C22 | semidirect |
| 27. C2×#213 | C22 | semidirect |
| 33. #833 | C22 | semidirect |
| 34. #823 | C22 | semidirect |
| 35. #822 | C22 | semidirect |
| 37. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 94. AGL(1,ℤ/8) | C2×D3 | semidirect |
| 257. C2×C3 | #472 | semidirect |
| 279. C3 | C2×#472 | semidirect |
| 285. C2 | #5199 | direct (N × H) |
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 |
| C2×#949 | 2 |
| C2×#948 | 2 |
| C22×#213 | 2 |
| C2×#833 | 2 |
| #5199 | 2 |
| C2×#823 | 2 |
| C2×#822 | 2 |
| C2×#472 | 3 |