Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70495 | C2 | semidirect |
| 5. #69726 | C2 | semidirect |
| 6. #67710 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 281. C3 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1492 | 2 |
| #71805 | 2 |
| #71801 | 2 |
| #70495 | 2 |
| #69726 | 2 |
| #67710 | 2 |
| #67656 | 2 |
| #9588 | 3 |