Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #5570 | C2 | semidirect |
| 4. #5166 | C2 | semidirect |
| 5. Dic3×SD16 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4768 | C2 | semidirect |
| 11. #4763 | C2 | semidirect |
| 230. C3 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5713 | 2 |
| #5570 | 2 |
| C3×#460 | 2 |
| #5166 | 2 |
| Dic3×SD16 | 2 |
| #5070 | 2 |
| C4×#216 | 2 |
| #4851 | 2 |
| #4830 | 2 |
| #4768 | 2 |
| #4763 | 2 |
| #3365 | 3 |