Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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×#424 | C2 | semidirect |
| 3. C2×#824 | C2 | semidirect |
| 5. #5004 | C2 | semidirect |
| 7. #4552 | C2 | semidirect |
| 25. #424 | D3 | semidirect |
| 195. C3 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C3×#424 | 2 |
| C2×#824 | 2 |
| C2×#823 | 2 |
| #5004 | 2 |
| #5001 | 2 |
| #4552 | 2 |
| #2046 | 3 |