Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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. #5517 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. Dic3×M16 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 8. #4768 | C2 | semidirect |
| 9. #4765 | C2 | semidirect |
| 22. #890 | C22 | semidirect |
| 23. #888 | C22 | semidirect |
| 28. #816 | C22 | semidirect |
| 29. #815 | C22 | semidirect |
| 30. C8×Dic3 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 204. C3 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| #5517 | 2 |
| C3×#418 | 2 |
| #5215 | 2 |
| #5120 | 2 |
| Dic3×M16 | 2 |
| #5004 | 2 |
| #4768 | 2 |
| #4765 | 2 |
| #3140 | 3 |