Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. C3×#2138 | C2 | semidirect |
| 3. #72080 | C2 | semidirect |
| 4. #71409 | C2 | semidirect |
| 5. #70665 | C2 | semidirect |
| 6. #70650 | C2 | semidirect |
| 7. #67808 | C2 | semidirect |
| 31. #2138 | D3 | semidirect |
| 342. C3 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83928 | 2 |
| C3×#2138 | 2 |
| #72080 | 2 |
| #71409 | 2 |
| #70665 | 2 |
| #70650 | 2 |
| #67808 | 2 |
| #13406 | 3 |