Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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×#3230 | C2 | semidirect |
| 4. #71839 | C2 | semidirect |
| 5. #71775 | C2 | semidirect |
| 7. #67736 | C2 | semidirect |
| 30. #3230 | D3 | semidirect |
| 349. C3 | #10292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3230 | 2 |
| #83355 | 2 |
| #83251 | 2 |
| #71839 | 2 |
| #71775 | 2 |
| #70774 | 2 |
| #67736 | 2 |
| #10292 | 3 |