Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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. C3×#501 | C2 | semidirect |
| 4. #5081 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 7. #4877 | C2 | semidirect |
| 9. #4857 | C2 | semidirect |
| 11. #4703 | C2 | semidirect |
| 47. #501 | D3 | semidirect |
| 236. C3 | #3236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×#125 | 2 |
| C3×#501 | 2 |
| #5081 | 2 |
| #5069 | 2 |
| #4884 | 2 |
| #4877 | 2 |
| #4862 | 2 |
| #4857 | 2 |
| #4705 | 2 |
| #4703 | 2 |
| #3236 | 3 |