Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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×C3×#393 | C2 | semidirect |
| 2. C2×#5231 | C2 | semidirect |
| 4. C2×#4947 | C2 | semidirect |
| 5. #76888 | C2 | direct (N × H) |
| 6. C2×#4673 | C2 | semidirect |
| 9. C23×C3×Q8 | C22 | semidirect |
| 10. C23×Dic6 | C22 | semidirect |
| 15. C3×#393 | C22 | semidirect |
| 16. C2×C3×#95 | C22 | semidirect |
| 17. #5231 | C22 | semidirect |
| 18. C2×C3⋊#95 | C22 | semidirect |
| 19. C2×C3⋊#95 | C22 | semidirect |
| 21. #4947 | C22 | semidirect |
| 22. #4673 | C22 | semidirect |
| 27. C2×#393 | D3 | semidirect |
| 32. C24×D3 | Q8 | semidirect |
| 36. C22×C3×Q8 | C23 | semidirect |
| 42. C22×Dic6 | C23 | semidirect |
| 51. C3×#95 | C23 | semidirect |
| 52. C3⋊#95 | C23 | semidirect |
| 53. C3⋊#95 | C23 | semidirect |
| 56. C23×Q8 | C2×D3 | semidirect |
| 64. #393 | C2×D3 | semidirect |
| 68. C2×#95 | C2×D3 | semidirect |
| 82. C23×D3 | C2×Q8 | semidirect |
| 113. C22×Q8 | C22×D3 | semidirect |
| 127. #95 | C22×D3 | semidirect |
| 245. C2×C3 | #2840 | semidirect |
| 268. C3 | C2×#2840 | semidirect |
| 271. C2 | #76888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#393 | 2 |
| C2×#5231 | 2 |
| C2×#4955 | 2 |
| C2×#4947 | 2 |
| #76888 | 2 |
| C2×#4673 | 2 |
| C2×#2840 | 3 |