Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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. #70794 | C2 | semidirect |
| 6. #69435 | C2 | semidirect |
| 7. #69433 | C2 | semidirect |
| 13. #5093 | C4 | semidirect |
| 14. #5080 | C4 | semidirect |
| 15. #5076 | C4 | semidirect |
| 16. #5070 | C4 | semidirect |
| 347. C3 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83290 | 2 |
| C3×#1505 | 2 |
| #71798 | 2 |
| #70813 | 2 |
| #70794 | 2 |
| #69435 | 2 |
| #69433 | 2 |
| #9766 | 3 |