Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #4716 | C2 | semidirect |
| 4. C3×#347 | C2 | semidirect |
| 6. #4517 | C2 | semidirect |
| 7. #4513 | C2 | semidirect |
| 20. Dic24 | C4 | semidirect |
| 21. #800 | C4 | semidirect |
| 28. #347 | D3 | semidirect |
| 125. C3 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4909 | 2 |
| #4717 | 2 |
| #4716 | 2 |
| C3×#347 | 2 |
| #4518 | 2 |
| #4517 | 2 |
| #4513 | 2 |
| #2180 | 3 |