Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×Q8×Dic3 | C2 | semidirect |
| 3. C3×#448 | C2 | semidirect |
| 4. #5227 | C2 | semidirect |
| 5. #5163 | C2 | semidirect |
| 6. Dic3×SD16 | C2 | semidirect |
| 7. #5034 | C2 | semidirect |
| 8. #4791 | C2 | semidirect |
| 9. #4788 | C2 | semidirect |
| 10. #4735 | C2 | semidirect |
| 11. #4718 | C2 | semidirect |
| 51. #448 | D3 | semidirect |
| 130. C3×Q8 | #41 | semidirect |
| 147. C2×Dic3 | SD16 | semidirect |
| 222. Q8 | #237 | semidirect |
| 274. C3 | #3103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| #5596 | 2 |
| C3×#448 | 2 |
| #5227 | 2 |
| #5163 | 2 |
| Dic3×SD16 | 2 |
| #5034 | 2 |
| #4791 | 2 |
| #4788 | 2 |
| #4735 | 2 |
| #4718 | 2 |
| #3103 | 3 |