Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1128 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 391 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. #83784 | C2 | semidirect |
| 3. #83780 | C2 | semidirect |
| 4. #72076 | C2 | semidirect |
| 5. C2×#4566 | C2 | semidirect |
| 8. C3×#578 | C4 | semidirect |
| 10. C3×#576 | C4 | semidirect |
| 17. #5106 | C22 | semidirect |
| 18. C2×#817 | C22 | semidirect |
| 19. C2×#812 | C22 | semidirect |
| 20. #4566 | C22 | semidirect |
| 21. #4566 | C22 | semidirect |
| 38. C3×#135 | C2×C4 | semidirect |
| 40. C2×C3×Q16 | C2×C4 | semidirect |
| 42. C2×C3×D8 | C2×C4 | semidirect |
| 59. #578 | Dic3 | semidirect |
| 61. #576 | Dic3 | semidirect |
| 119. #135 | C2×Dic3 | semidirect |
| 121. C2×Q16 | C2×Dic3 | semidirect |
| 123. C2×D8 | C2×Dic3 | semidirect |
| 246. C3 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3584 | 2 |
| #83784 | 2 |
| #83780 | 2 |
| #72076 | 2 |
| C2×#4566 | 2 |
| #33388 | 3 |