Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 272. C3 | #9585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70777 | 2 |
| #70753 | 2 |
| #69856 | 2 |
| #69738 | 2 |
| #69724 | 2 |
| C3×#1278 | 2 |
| #67669 | 2 |
| #9585 | 3 |