Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 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. #82920 | C2 | semidirect |
| 3. C3×#1504 | C2 | semidirect |
| 4. #69970 | C2 | semidirect |
| 5. C2×#4451 | C2 | semidirect |
| 6. #67688 | C2 | semidirect |
| 7. #67613 | C2 | semidirect |
| 19. #5046 | C4 | semidirect |
| 20. #5044 | C4 | semidirect |
| 22. #5036 | C4 | semidirect |
| 23. #5034 | C4 | semidirect |
| 38. #1504 | D3 | semidirect |
| 480. C3 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82929 | 2 |
| #82920 | 2 |
| C3×#1504 | 2 |
| #69970 | 2 |
| C2×#4451 | 2 |
| #67688 | 2 |
| #67613 | 2 |
| #9264 | 3 |