Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#887 | C2 | semidirect |
| 3. C3×#483 | C2 | semidirect |
| 4. #5050 | C2 | semidirect |
| 6. #4857 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4798 | C2 | semidirect |
| 9. #4790 | C2 | semidirect |
| 11. #4718 | C2 | semidirect |
| 46. #483 | D3 | semidirect |
| 257. C3 | #3108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5624 | 2 |
| C2×#887 | 2 |
| C3×#483 | 2 |
| #5050 | 2 |
| #4967 | 2 |
| #4857 | 2 |
| #4852 | 2 |
| #4798 | 2 |
| #4790 | 2 |
| #4738 | 2 |
| #4718 | 2 |
| #3108 | 3 |