Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#214 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. C2×#907 | C2 | semidirect |
| 5. C2×C3×#100 | C2 | semidirect |
| 6. C2×#824 | C2 | semidirect |
| 7. C2×#822 | C2 | semidirect |
| 8. #4748 | C2 | direct (N × H) |
| 19. C2×#214 | C22 | semidirect |
| 26. #909 | C22 | semidirect |
| 28. #907 | C22 | semidirect |
| 33. C3×#100 | C22 | semidirect |
| 34. #824 | C22 | semidirect |
| 35. #822 | C22 | semidirect |
| 43. C2×#100 | D3 | semidirect |
| 113. #100 | C2×D3 | semidirect |
| 251. C2×C3 | #471 | semidirect |
| 270. C3 | C2×#471 | semidirect |
| 275. C2 | #4748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#214 | 2 |
| C2×#932 | 2 |
| C2×#909 | 2 |
| C2×#907 | 2 |
| C2×C3×#100 | 2 |
| C2×#824 | 2 |
| C2×#822 | 2 |
| #4748 | 2 |
| C2×#471 | 3 |