Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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×#2912 | C2 | semidirect |
| 3. #83780 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. C2×#4488 | C2 | semidirect |
| 10. #5753 | C4 | semidirect |
| 11. #5752 | C4 | semidirect |
| 16. C3×#427 | C22 | semidirect |
| 17. C2×C3×#106 | C22 | semidirect |
| 19. C2×#812 | C22 | semidirect |
| 20. #4488 | C22 | semidirect |
| 21. #4488 | C22 | semidirect |
| 24. #2912 | D3 | semidirect |
| 44. C2×Dic12 | C2×C4 | semidirect |
| 47. #904 | C2×C4 | semidirect |
| 49. C2×D24 | C2×C4 | semidirect |
| 69. #427 | C2×D3 | semidirect |
| 70. C2×#106 | C2×D3 | semidirect |
| 246. C3 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87163 | 2 |
| C3×#2912 | 2 |
| #83780 | 2 |
| #70656 | 2 |
| C2×#4488 | 2 |
| #33388 | 3 |