Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 125 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×#837 | C2 | semidirect |
| 3. #5232 | C2 | semidirect |
| 4. #5229 | C2 | semidirect |
| 5. C2×#836 | C2 | semidirect |
| 9. C3×2−1+4 | C4 | semidirect |
| 60. 2−1+4 | Dic3 | semidirect |
| 196. C3 | #1793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×2−1+4 | 2 |
| C2×#837 | 2 |
| #5232 | 2 |
| #5229 | 2 |
| C2×#836 | 2 |
| #1793 | 3 |