Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5722 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 6. #4767 | C2 | semidirect |
| 7. #4765 | C2 | semidirect |
| 8. #4759 | C2 | semidirect |
| 9. #4757 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 232. C3 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| #5713 | 2 |
| C3×#486 | 2 |
| #5091 | 2 |
| #5075 | 2 |
| #4767 | 2 |
| #4765 | 2 |
| #4759 | 2 |
| #4757 | 2 |
| C4×Dic12 | 2 |
| #4679 | 2 |
| #3375 | 3 |