Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. C2×#5115 | C2 | semidirect |
| 2. C2×C3×C22⋊C16 | C2 | semidirect |
| 3. #71413 | C2 | semidirect |
| 4. #69108 | C2 | semidirect |
| 5. #69095 | C2 | semidirect |
| 9. C22×D24 | C22 | semidirect |
| 10. C22×C3×C16 | C22 | semidirect |
| 14. #5115 | C22 | semidirect |
| 16. C2×#818 | C22 | semidirect |
| 17. C2×D48 | C22 | semidirect |
| 18. C3×C22⋊C16 | C22 | semidirect |
| 19. #4509 | C22 | semidirect |
| 20. #4504 | C22 | semidirect |
| 25. C2×C22⋊C16 | D3 | semidirect |
| 54. C22×C16 | C2×D3 | semidirect |
| 63. C22⋊C16 | C2×D3 | semidirect |
| 120. C23×C3 | D16 | semidirect |
| 199. C23 | D48 | semidirect |
| 244. C3 | #33752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5115 | 2 |
| C2×C3×C22⋊C16 | 2 |
| #71413 | 2 |
| #69108 | 2 |
| #69095 | 2 |
| #33752 | 3 |