Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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×#489 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5055 | C2 | semidirect |
| 6. #4803 | C2 | semidirect |
| 7. #4792 | C2 | semidirect |
| 8. #4771 | C2 | semidirect |
| 9. #4760 | C2 | semidirect |
| 10. #4714 | C2 | semidirect |
| 11. #4707 | C2 | semidirect |
| 49. #489 | D3 | semidirect |
| 274. C3 | #3141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5668 | 2 |
| C3×#489 | 2 |
| #5089 | 2 |
| #5055 | 2 |
| #4803 | 2 |
| #4792 | 2 |
| #4771 | 2 |
| #4760 | 2 |
| #4714 | 2 |
| #4707 | 2 |
| #3141 | 3 |