Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83133 | C2 | semidirect |
| 3. #71766 | C2 | semidirect |
| 4. #71760 | C2 | semidirect |
| 5. #71747 | C2 | semidirect |
| 6. #67758 | C2 | semidirect |
| 7. #67754 | C2 | semidirect |
| 398. C3 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3217 | 2 |
| #83133 | 2 |
| #71766 | 2 |
| #71760 | 2 |
| #71747 | 2 |
| #67758 | 2 |
| #67754 | 2 |
| #9340 | 3 |