Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #70813 | C2 | semidirect |
| 5. #69546 | C2 | semidirect |
| 6. #67751 | C2 | semidirect |
| 7. #67630 | C2 | semidirect |
| 13. #5069 | C4 | semidirect |
| 14. #5064 | C4 | semidirect |
| 15. #5060 | C4 | semidirect |
| 16. #5055 | C4 | semidirect |
| 390. C3 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83138 | 2 |
| #83128 | 2 |
| C3×#1512 | 2 |
| #70813 | 2 |
| #69546 | 2 |
| #67751 | 2 |
| #67630 | 2 |
| #9431 | 3 |