Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #5539 | C2 | semidirect |
| 5. #5009 | C2 | semidirect |
| 6. #4878 | C2 | semidirect |
| 7. #4874 | C2 | semidirect |
| 8. #4763 | C2 | semidirect |
| 9. #4761 | C2 | semidirect |
| 10. #4683 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 57. C3×D8 | Q8 | semidirect |
| 134. D8 | Dic6 | semidirect |
| 212. C3 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5539 | 2 |
| C3×C4×D8 | 2 |
| Dic3×D8 | 2 |
| #5009 | 2 |
| #4878 | 2 |
| #4874 | 2 |
| #4763 | 2 |
| #4761 | 2 |
| #4683 | 2 |
| C8×Dic6 | 2 |
| #3380 | 3 |