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. C2×C3×#100 | C2 | semidirect |
| 3. C2×#833 | C2 | semidirect |
| 4. C2×#824 | C2 | semidirect |
| 5. #5126 | C2 | semidirect |
| 25. C2×#100 | 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×#237 | 2 |
| C2×C3×#100 | 2 |
| C2×#833 | 2 |
| C2×#824 | 2 |
| #5126 | 2 |
| #1785 | 3 |