Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 139 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. C3×M16 | Q16 | semidirect |
| 145. M16 | Dic12 | semidirect |
| 208. C3 | #9798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4699 | 2 |
| C3×C8×M16 | 2 |
| #70779 | 2 |
| #69879 | 2 |
| #69731 | 2 |
| #9798 | 3 |