Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #67466 | C2 | semidirect |
| 95. Dic12 | M16 | semidirect |
| 230. C3 | #11664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic12 | 2 |
| C3×#1566 | 2 |
| #69745 | 2 |
| #67466 | 2 |
| #11664 | 3 |