Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #68063 | C2 | semidirect |
| 5. #67476 | C2 | semidirect |
| 6. #67474 | C2 | semidirect |
| 7. #67439 | C2 | semidirect |
| 133. C3×C8 | SD32 | semidirect |
| 191. C8 | #827 | semidirect |
| 210. C3 | #12420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D8 | 2 |
| #70892 | 2 |
| #70887 | 2 |
| #68063 | 2 |
| #67476 | 2 |
| #67474 | 2 |
| #67439 | 2 |
| #12420 | 3 |