Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1471 | C2 | semidirect |
| 3. #71673 | C2 | semidirect |
| 4. #69982 | C2 | semidirect |
| 5. #69977 | C2 | semidirect |
| 6. #69948 | C2 | semidirect |
| 7. #69921 | C2 | semidirect |
| 10. C22×#213 | C4 | semidirect |
| 15. C2×#832 | C4 | semidirect |
| 24. C2×#809 | C4 | semidirect |
| 25. C2×#807 | C4 | semidirect |
| 38. #1471 | D3 | semidirect |
| 440. C3 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5038 | 2 |
| C3×#1471 | 2 |
| #71673 | 2 |
| #69982 | 2 |
| #69977 | 2 |
| #69948 | 2 |
| #69921 | 2 |
| #9818 | 3 |