Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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. C3×#1566 | C2 | semidirect |
| 3. #70524 | C2 | semidirect |
| 5. #70507 | C2 | semidirect |
| 7. C8×#208 | C2 | semidirect |
| 30. #1566 | D3 | semidirect |
| 121. #208 | SD16 | semidirect |
| 190. C3×C8 | #100 | semidirect |
| 279. C8 | #823 | semidirect |
| 301. C3 | #9793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4693 | 2 |
| C3×#1566 | 2 |
| #70524 | 2 |
| #70521 | 2 |
| #70507 | 2 |
| #70502 | 2 |
| C8×#208 | 2 |
| #9793 | 3 |