Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
494 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#5055 | C2 | semidirect |
| 3. #79268 | C2 | semidirect |
| 4. C3×#1469 | C2 | semidirect |
| 5. #70824 | C2 | semidirect |
| 6. #70806 | C2 | semidirect |
| 7. #67742 | C2 | semidirect |
| 37. #1469 | D3 | semidirect |
| 358. C3 | #10140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82947 | 2 |
| C2×#5055 | 2 |
| #79268 | 2 |
| C3×#1469 | 2 |
| #70824 | 2 |
| #70806 | 2 |
| #67742 | 2 |
| #10140 | 3 |