Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×Dic12 | C2 | semidirect |
| 4. #5516 | C2 | semidirect |
| 5. C3×#424 | C2 | semidirect |
| 6. #5120 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4845 | C2 | semidirect |
| 40. #424 | D3 | semidirect |
| 218. C3 | #3044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| C22×Dic12 | 2 |
| #5526 | 2 |
| #5516 | 2 |
| C3×#424 | 2 |
| #5120 | 2 |
| #5113 | 2 |
| #4849 | 2 |
| #4845 | 2 |
| #3044 | 3 |