Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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. #4909 | C2 | semidirect |
| 3. #4700 | C2 | semidirect |
| 4. #4696 | C2 | semidirect |
| 5. C3×#364 | C2 | semidirect |
| 6. #4517 | C2 | semidirect |
| 7. #4516 | C2 | semidirect |
| 28. #364 | D3 | semidirect |
| 144. C3 | #2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4909 | 2 |
| #4908 | 2 |
| #4700 | 2 |
| #4696 | 2 |
| C3×#364 | 2 |
| #4517 | 2 |
| #4516 | 2 |
| #2212 | 3 |