Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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×#926 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 12. #930 | C4 | semidirect |
| 18. #924 | C4 | semidirect |
| 25. #407 | D3 | semidirect |
| 54. C4×Dic3 | D4 | semidirect |
| 190. C3 | #1897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5791 | 2 |
| C2×#926 | 2 |
| C3×#407 | 2 |
| C2×#825 | 2 |
| #4555 | 2 |
| #1897 | 3 |