Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. C22×#214 | C2 | semidirect |
| 3. C2×#875 | C2 | semidirect |
| 4. C3×#390 | C2 | semidirect |
| 5. C2×#810 | C2 | semidirect |
| 6. C2×#809 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 33. #390 | D3 | semidirect |
| 259. C3 | #2012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#214 | 2 |
| C22×#213 | 2 |
| C2×#875 | 2 |
| C3×#390 | 2 |
| C2×#810 | 2 |
| C2×#809 | 2 |
| #4524 | 2 |
| #2012 | 3 |