Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#4682 | C2 | semidirect |
| 4. #70778 | C2 | semidirect |
| 5. #69877 | C2 | semidirect |
| 7. C3×#1278 | C2 | semidirect |
| 36. #1278 | D3 | semidirect |
| 345. C3 | #10174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79268 | 2 |
| #78538 | 2 |
| C2×#4682 | 2 |
| #70778 | 2 |
| #69877 | 2 |
| #69735 | 2 |
| C3×#1278 | 2 |
| #10174 | 3 |