Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #5731 | C2 | semidirect |
| 3. C3×#491 | C2 | semidirect |
| 4. #5085 | C2 | semidirect |
| 5. #5065 | C2 | semidirect |
| 6. #4817 | C2 | semidirect |
| 7. #4812 | C2 | semidirect |
| 8. #4807 | C2 | semidirect |
| 9. #4788 | C2 | semidirect |
| 10. #4713 | C2 | semidirect |
| 11. #4708 | C2 | semidirect |
| 44. #491 | D3 | semidirect |
| 212. C3 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5731 | 2 |
| #5697 | 2 |
| C3×#491 | 2 |
| #5085 | 2 |
| #5065 | 2 |
| #4817 | 2 |
| #4812 | 2 |
| #4807 | 2 |
| #4788 | 2 |
| #4713 | 2 |
| #4708 | 2 |
| #3174 | 3 |