Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #73308 | C2 | semidirect |
| 4. #70780 | C2 | semidirect |
| 5. #70778 | C2 | semidirect |
| 7. C3×#1276 | C2 | semidirect |
| 36. #1276 | D3 | semidirect |
| 341. C3 | #10286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79269 | 2 |
| #79268 | 2 |
| #73308 | 2 |
| #70780 | 2 |
| #70778 | 2 |
| #69395 | 2 |
| C3×#1276 | 2 |
| #10286 | 3 |