Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #5827 | C2 | semidirect |
| 3. C3×#408 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. #5106 | C2 | semidirect |
| 8. #4737 | C2 | semidirect |
| 9. #4737 | C2 | semidirect |
| 10. #4736 | C2 | semidirect |
| 11. #4735 | C2 | semidirect |
| 27. #926 | C22 | semidirect |
| 29. C2×C4⋊Dic3 | C22 | semidirect |
| 30. C3×C22⋊C8 | C22 | semidirect |
| 31. C3×C22⋊C8 | C22 | semidirect |
| 36. #818 | C22 | semidirect |
| 37. #818 | C22 | semidirect |
| 38. #818 | C22 | semidirect |
| 39. #817 | C22 | semidirect |
| 40. #817 | C22 | semidirect |
| 41. #817 | C22 | semidirect |
| 52. #408 | D3 | semidirect |
| 116. C22⋊C8 | C2×D3 | semidirect |
| 117. C22⋊C8 | C2×D3 | semidirect |
| 262. C3 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5830 | 2 |
| #5827 | 2 |
| C3×#408 | 2 |
| #5131 | 2 |
| #5121 | 2 |
| C2×#821 | 2 |
| #5106 | 2 |
| #4737 | 2 |
| #4736 | 2 |
| #4735 | 2 |
| #3096 | 3 |