Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 67 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. #71087 | C2 | semidirect |
| 4. #70487 | C2 | semidirect |
| 5. #67776 | C2 | semidirect |
| 7. #67709 | C2 | semidirect |
| 328. C3 | #12163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3250 | 2 |
| #71087 | 2 |
| #71077 | 2 |
| #70487 | 2 |
| #67776 | 2 |
| #67774 | 2 |
| #67709 | 2 |
| #12163 | 3 |