Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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. #83288 | C2 | semidirect |
| 3. #79312 | C2 | semidirect |
| 4. C3×#1484 | C2 | semidirect |
| 5. #69879 | C2 | semidirect |
| 6. #69859 | C2 | semidirect |
| 7. #67743 | C2 | semidirect |
| 37. #1484 | D3 | semidirect |
| 370. C3 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83313 | 2 |
| #83288 | 2 |
| #79312 | 2 |
| C3×#1484 | 2 |
| #69879 | 2 |
| #69859 | 2 |
| #67743 | 2 |
| #10106 | 3 |