Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 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. #5479 | C2 | semidirect |
| 2. C2×C4×D12 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4847 | C2 | semidirect |
| 5. #4844 | C2 | semidirect |
| 6. #4735 | C2 | semidirect |
| 8. #4731 | C2 | semidirect |
| 9. #4722 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 25. #875 | C22 | semidirect |
| 30. C4×D12 | C22 | semidirect |
| 32. #870 | C22 | semidirect |
| 33. C4×Dic6 | C22 | semidirect |
| 34. C3×C4⋊C8 | C22 | semidirect |
| 37. C3×C4×C8 | C22 | semidirect |
| 40. #821 | C22 | semidirect |
| 41. #818 | C22 | semidirect |
| 42. #817 | C22 | semidirect |
| 43. #816 | C22 | semidirect |
| 54. #431 | D3 | semidirect |
| 117. C4⋊C8 | C2×D3 | semidirect |
| 124. C4×C8 | C2×D3 | semidirect |
| 274. C3 | #3105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C2×C4×D12 | 2 |
| C3×#431 | 2 |
| #4847 | 2 |
| #4844 | 2 |
| #4735 | 2 |
| #4732 | 2 |
| #4731 | 2 |
| #4722 | 2 |
| C4×D24 | 2 |
| C4×#204 | 2 |
| #3105 | 3 |