Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5585 | C2 | semidirect |
| 2. D4×Dic6 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5165 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4870 | C2 | semidirect |
| 8. #4794 | C2 | semidirect |
| 9. #4785 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 52. C4×SD16 | D3 | semidirect |
| 243. C3 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| D4×Dic6 | 2 |
| C3×C4×SD16 | 2 |
| #5165 | 2 |
| #5020 | 2 |
| #5015 | 2 |
| #4870 | 2 |
| #4794 | 2 |
| #4785 | 2 |
| #4694 | 2 |
| #4679 | 2 |
| #3373 | 3 |