Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
678 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 111 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. #83270 | C2 | semidirect |
| 3. #73313 | C2 | semidirect |
| 4. C3×#1962 | C2 | semidirect |
| 5. #70506 | C2 | semidirect |
| 6. #70502 | C2 | semidirect |
| 7. #67611 | C2 | semidirect |
| 33. #1962 | D3 | semidirect |
| 138. C3×C42 | D8 | semidirect |
| 281. C42 | #213 | semidirect |
| 376. C3 | #10284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83302 | 2 |
| #83270 | 2 |
| #73313 | 2 |
| C3×#1962 | 2 |
| #70506 | 2 |
| #70502 | 2 |
| #67611 | 2 |
| #10284 | 3 |