Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #69857 | C2 | semidirect |
| 5. #69838 | C2 | semidirect |
| 6. #67668 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 406. C3 | #9051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83152 | 2 |
| #83130 | 2 |
| C3×#1524 | 2 |
| #69857 | 2 |
| #69838 | 2 |
| #67668 | 2 |
| #67662 | 2 |
| #9051 | 3 |