Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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×#932 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. #5748 | C2 | semidirect |
| 4. #5745 | C2 | semidirect |
| 5. C2×C3×#100 | C2 | semidirect |
| 6. #5132 | C2 | semidirect |
| 7. #5124 | C2 | semidirect |
| 8. #4749 | C2 | semidirect |
| 9. #4748 | C2 | semidirect |
| 17. C2×#214 | C22 | semidirect |
| 23. C2×#213 | C22 | semidirect |
| 27. #909 | C22 | semidirect |
| 29. #908 | C22 | semidirect |
| 30. #907 | C22 | semidirect |
| 34. C3×#100 | C22 | semidirect |
| 35. #824 | C22 | semidirect |
| 36. #823 | C22 | semidirect |
| 37. #822 | C22 | semidirect |
| 46. C2×#100 | D3 | semidirect |
| 119. #100 | C2×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×#932 | 2 |
| #5748 | 2 |
| #5745 | 2 |
| C2×C3×#100 | 2 |
| #5132 | 2 |
| #5124 | 2 |
| #4749 | 2 |
| #4748 | 2 |
| #3068 | 3 |