Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
222 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 50. C3×M16 | C16 | semidirect |
| 105. M16 | C3⋊C16 | semidirect |
| 169. C3 | #7209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×M16 | 2 |
| #69744 | 2 |
| C2×C4⋊(C3⋊C16) | 2 |
| #7209 | 3 |