Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
478 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 111 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×#1835 | C2 | semidirect |
| 3. #69726 | C2 | semidirect |
| 4. #69545 | C2 | semidirect |
| 11. #4699 | C4 | semidirect |
| 13. #4695 | C4 | semidirect |
| 14. #4693 | C4 | semidirect |
| 19. #1835 | D3 | semidirect |
| 182. C3 | #9760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78467 | 2 |
| C3×#1835 | 2 |
| #69726 | 2 |
| #69545 | 2 |
| #9760 | 3 |