Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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. C3×#407 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. C2×#824 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 26. #407 | D3 | semidirect |
| 200. C3 | #1785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C3×#407 | 2 |
| #5207 | 2 |
| C2×#824 | 2 |
| C2×#823 | 2 |
| #1785 | 3 |