Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #71825 | C2 | semidirect |
| 5. #67656 | C2 | semidirect |
| 236. C3 | #9067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3131 | 2 |
| #83278 | 2 |
| #71825 | 2 |
| #71797 | 2 |
| #67656 | 2 |
| #9067 | 3 |