Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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. #67795 | C2 | semidirect |
| 5. #67786 | C2 | semidirect |
| 278. C3 | #13612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3223 | 2 |
| #71873 | 2 |
| #71872 | 2 |
| #67795 | 2 |
| #67786 | 2 |
| #13612 | 3 |