Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 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 |
|---|---|---|
| 2. C3×#1810 | C2 | semidirect |
| 3. #71967 | C2 | semidirect |
| 4. #69980 | C2 | semidirect |
| 6. #69972 | C2 | semidirect |
| 12. C22×#204 | C4 | semidirect |
| 22. C2×#821 | C4 | semidirect |
| 23. C2×#817 | C4 | semidirect |
| 24. C2×#816 | C4 | semidirect |
| 33. #1810 | D3 | semidirect |
| 423. C3 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5114 | 2 |
| C3×#1810 | 2 |
| #71967 | 2 |
| #69980 | 2 |
| #69977 | 2 |
| #69972 | 2 |
| #69970 | 2 |
| #9816 | 3 |