Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 89 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. #74265 | C2 | semidirect |
| 4. #70824 | C2 | semidirect |
| 6. C3×#1288 | C2 | semidirect |
| 7. #67666 | C2 | semidirect |
| 18. #4699 | C4 | semidirect |
| 19. #4693 | C4 | semidirect |
| 32. #1288 | D3 | semidirect |
| 307. C3 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78538 | 2 |
| #74265 | 2 |
| #70835 | 2 |
| #70824 | 2 |
| #69564 | 2 |
| C3×#1288 | 2 |
| #67666 | 2 |
| #9429 | 3 |