Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. D3×C4⋊Q8 | C2 | semidirect |
| 3. C3×#491 | C2 | semidirect |
| 4. #5086 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 6. #4818 | C2 | semidirect |
| 7. #4809 | C2 | semidirect |
| 9. #4795 | C2 | semidirect |
| 10. #4715 | C2 | semidirect |
| 11. #4705 | C2 | semidirect |
| 49. #491 | D3 | semidirect |
| 265. C3 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5691 | 2 |
| C3×#491 | 2 |
| #5086 | 2 |
| #5069 | 2 |
| #4818 | 2 |
| #4809 | 2 |
| #4806 | 2 |
| #4795 | 2 |
| #4715 | 2 |
| #4705 | 2 |
| #3218 | 3 |