Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C3×#2253 | C2 | semidirect |
| 3. #67577 | C2 | semidirect |
| 4. #67508 | C2 | semidirect |
| 14. #2253 | D3 | semidirect |
| 111. C3 | #13723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2253 | 2 |
| #69060 | 2 |
| #67577 | 2 |
| #67508 | 2 |
| #13723 | 3 |