Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×C3×#103 | C2 | semidirect |
| 3. #5229 | C2 | semidirect |
| 5. C2×Dic3⋊C8 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 28. C2×#103 | D3 | semidirect |
| 116. C2×Dic3 | SD16 | semidirect |
| 250. C3 | #2055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#215 | 2 |
| C2×C3×#103 | 2 |
| #5229 | 2 |
| C2×#821 | 2 |
| C2×Dic3⋊C8 | 2 |
| #4988 | 2 |
| #4529 | 2 |
| #2055 | 3 |