Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 89. Dic6 | Q16 | semidirect |
| 163. C3 | #1645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| C3×#487 | 2 |
| #5094 | 2 |
| #5090 | 2 |
| #4546 | 2 |
| #4456 | 2 |
| #1645 | 3 |