Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5470 | C2 | semidirect |
| 3. C3×#432 | C2 | semidirect |
| 4. #4849 | C2 | semidirect |
| 5. #4848 | C2 | semidirect |
| 6. #4733 | C2 | semidirect |
| 7. #4715 | C2 | semidirect |
| 8. #4714 | C2 | semidirect |
| 41. #432 | D3 | semidirect |
| 213. C3 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| #5470 | 2 |
| C3×#432 | 2 |
| #4849 | 2 |
| #4848 | 2 |
| #4733 | 2 |
| #4715 | 2 |
| #4714 | 2 |
| #3216 | 3 |