Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 72. #216 | Q8 | semidirect |
| 217. C3 | #3387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| Q8×Dic6 | 2 |
| #5094 | 2 |
| #5080 | 2 |
| #5064 | 2 |
| #5063 | 2 |
| #5030 | 2 |
| C4×#216 | 2 |
| #5024 | 2 |
| #5021 | 2 |
| #5020 | 2 |
| #3387 | 3 |