Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5543 | C2 | semidirect |
| 3. C3×#436 | C2 | semidirect |
| 4. #5137 | C2 | semidirect |
| 5. #5133 | C2 | semidirect |
| 6. #4849 | C2 | semidirect |
| 7. #4842 | C2 | semidirect |
| 8. #4733 | C2 | semidirect |
| 9. #4721 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 51. #436 | D3 | semidirect |
| 247. C3 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5551 | 2 |
| #5543 | 2 |
| C3×#436 | 2 |
| #5137 | 2 |
| #5133 | 2 |
| #4849 | 2 |
| #4842 | 2 |
| #4733 | 2 |
| #4721 | 2 |
| C4×#204 | 2 |
| #4681 | 2 |
| #3331 | 3 |