Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C3×#477 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 7. #4875 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 11. #4795 | C2 | semidirect |
| 48. #477 | D3 | semidirect |
| 143. C4×D3 | Q16 | semidirect |
| 254. C3 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5578 | 2 |
| C3×#477 | 2 |
| #5091 | 2 |
| #5031 | 2 |
| #4887 | 2 |
| #4875 | 2 |
| #4849 | 2 |
| D3×C4⋊C8 | 2 |
| #4813 | 2 |
| #4795 | 2 |
| #3249 | 3 |