Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 2. #79337 | C2 | semidirect |
| 3. C3×#1555 | C2 | semidirect |
| 4. #71760 | C2 | semidirect |
| 5. #70811 | C2 | semidirect |
| 6. #67754 | C2 | semidirect |
| 7. #67753 | C2 | semidirect |
| 29. #1555 | D3 | semidirect |
| 320. C3 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83163 | 2 |
| #79337 | 2 |
| C3×#1555 | 2 |
| #71760 | 2 |
| #70811 | 2 |
| #67754 | 2 |
| #67753 | 2 |
| #9423 | 3 |