Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic12 | C2 | semidirect |
| 4. #5137 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #5116 | C2 | semidirect |
| 7. #5106 | C2 | semidirect |
| 172. C3 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5825 | 2 |
| C22×Dic12 | 2 |
| #5137 | 2 |
| #5120 | 2 |
| #5116 | 2 |
| #5106 | 2 |
| #3059 | 3 |