Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 117 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. #79263 | C2 | semidirect |
| 5. #70528 | C2 | semidirect |
| 6. #67746 | C2 | semidirect |
| 7. #67715 | C2 | semidirect |
| 356. C3 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83179 | 2 |
| #79263 | 2 |
| C3×#1545 | 2 |
| #71759 | 2 |
| #70528 | 2 |
| #67746 | 2 |
| #67715 | 2 |
| #9398 | 3 |