Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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×#1744 | C2 | semidirect |
| 3. #69735 | C2 | semidirect |
| 4. #69731 | C2 | semidirect |
| 5. #69395 | C2 | semidirect |
| 14. #4695 | C4 | semidirect |
| 15. #4694 | C4 | semidirect |
| 17. #4682 | C4 | semidirect |
| 23. #1744 | D3 | semidirect |
| 86. C3×C42 | D8 | semidirect |
| 178. C42 | D24 | semidirect |
| 247. C3 | #9847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×#1744 | 2 |
| #69735 | 2 |
| #69731 | 2 |
| #69395 | 2 |
| #9847 | 3 |