Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #83323 | C2 | semidirect |
| 4. #71839 | C2 | semidirect |
| 6. #70778 | C2 | semidirect |
| 7. #67736 | C2 | semidirect |
| 144. C4×Dic3 | SD16 | semidirect |
| 355. C3 | #10294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3208 | 2 |
| #83323 | 2 |
| #83184 | 2 |
| #71839 | 2 |
| #71759 | 2 |
| #70778 | 2 |
| #67736 | 2 |
| #10294 | 3 |