Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. D4×Dic6 | C2 | semidirect |
| 3. C3×#436 | C2 | semidirect |
| 4. #5134 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #4850 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 8. #4738 | C2 | semidirect |
| 9. #4723 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 51. #436 | D3 | semidirect |
| 247. C3 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5563 | 2 |
| D4×Dic6 | 2 |
| C3×#436 | 2 |
| #5134 | 2 |
| #5120 | 2 |
| #4850 | 2 |
| #4841 | 2 |
| #4738 | 2 |
| #4723 | 2 |
| C4×#204 | 2 |
| #4681 | 2 |
| #3329 | 3 |