Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
276 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 227. C3 | #12410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic12 | 2 |
| #70945 | 2 |
| #69296 | 2 |
| #69044 | 2 |
| C3×Q8⋊C16 | 2 |
| #67565 | 2 |
| #67505 | 2 |
| #12410 | 3 |