Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 107 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×#4681 | C2 | semidirect |
| 5. #70524 | C2 | semidirect |
| 6. #70506 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 144. #208 | SD16 | semidirect |
| 341. C3 | #10170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83317 | 2 |
| #83288 | 2 |
| C2×#4681 | 2 |
| C3×#1492 | 2 |
| #70524 | 2 |
| #70506 | 2 |
| #67656 | 2 |
| #10170 | 3 |