Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
470 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #79264 | C2 | semidirect |
| 4. #70486 | C2 | semidirect |
| 6. C3×#1301 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 19. #4849 | C4 | semidirect |
| 20. #4848 | C4 | semidirect |
| 33. #1301 | D3 | semidirect |
| 360. C3 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79264 | 2 |
| #79067 | 2 |
| #70790 | 2 |
| #70486 | 2 |
| #70426 | 2 |
| C3×#1301 | 2 |
| #67713 | 2 |
| #9310 | 3 |