Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 690 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 |
|---|---|---|
| 1. #83317 | C2 | semidirect |
| 3. C2×#4693 | C2 | semidirect |
| 4. C3×#1492 | C2 | semidirect |
| 5. #70524 | C2 | semidirect |
| 6. #70502 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 35. #1492 | D3 | semidirect |
| 147. #208 | SD16 | semidirect |
| 368. C3 | #10146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83317 | 2 |
| #83287 | 2 |
| C2×#4693 | 2 |
| C3×#1492 | 2 |
| #70524 | 2 |
| #70502 | 2 |
| #67656 | 2 |
| #10146 | 3 |