Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 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. C2×C4×Dic6 | C2 | semidirect |
| 3. #5094 | C2 | semidirect |
| 4. #5075 | C2 | semidirect |
| 5. #5040 | C2 | semidirect |
| 6. #5034 | C2 | semidirect |
| 7. C4×#214 | C2 | semidirect |
| 8. #4925 | C2 | semidirect |
| 108. C2×C3×C4 | SD16 | semidirect |
| 121. Dic6 | #41 | semidirect |
| 188. C2×C4 | #214 | semidirect |
| 217. C3 | #3103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C2×C4×Dic6 | 2 |
| #5094 | 2 |
| #5075 | 2 |
| #5040 | 2 |
| #5034 | 2 |
| C4×#214 | 2 |
| #4925 | 2 |
| #3103 | 3 |