Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic6 | C2 | semidirect |
| 3. C3×#432 | C2 | semidirect |
| 4. #4845 | C2 | semidirect |
| 5. #4829 | C2 | semidirect |
| 6. #4739 | C2 | semidirect |
| 9. #4722 | C2 | semidirect |
| 10. #4716 | C2 | semidirect |
| 11. #4710 | C2 | semidirect |
| 54. #432 | D3 | semidirect |
| 257. C3 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C2×C4×Dic6 | 2 |
| C3×#432 | 2 |
| #4845 | 2 |
| #4829 | 2 |
| #4739 | 2 |
| #4738 | 2 |
| #4735 | 2 |
| #4722 | 2 |
| #4716 | 2 |
| #4710 | 2 |
| #3117 | 3 |