Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. C3×#3206 | C2 | semidirect |
| 3. #83203 | C2 | semidirect |
| 4. #71797 | C2 | semidirect |
| 5. #71790 | C2 | semidirect |
| 6. #70761 | C2 | semidirect |
| 7. #67743 | C2 | semidirect |
| 33. #3206 | D3 | semidirect |
| 370. C3 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3206 | 2 |
| #83313 | 2 |
| #83203 | 2 |
| #71797 | 2 |
| #71790 | 2 |
| #70761 | 2 |
| #67743 | 2 |
| #10106 | 3 |