Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 5. #4973 | C2 | semidirect |
| 6. C2×#810 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 244. C3 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C22×#214 | 2 |
| C22×Dic12 | 2 |
| C2×C3×#102 | 2 |
| #4973 | 2 |
| C2×#810 | 2 |
| #4550 | 2 |
| #2015 | 3 |