Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 6. #4878 | C2 | semidirect |
| 7. #4874 | C2 | semidirect |
| 8. #4856 | C2 | semidirect |
| 40. C2×C3×C8 | Q8 | semidirect |
| 56. #208 | Q8 | semidirect |
| 97. C2×C8 | Dic6 | semidirect |
| 156. C3 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5519 | 2 |
| C3×#427 | 2 |
| C2×#818 | 2 |
| #5101 | 2 |
| #4995 | 2 |
| #4878 | 2 |
| #4874 | 2 |
| #4856 | 2 |
| #3164 | 3 |