Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
464 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 3. C3×#1518 | C2 | semidirect |
| 4. #71824 | C2 | semidirect |
| 6. #67745 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 13. #5087 | C4 | semidirect |
| 14. #5084 | C4 | semidirect |
| 31. #1518 | D3 | semidirect |
| 344. C3 | #9307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83350 | 2 |
| #79288 | 2 |
| C3×#1518 | 2 |
| #71824 | 2 |
| #69556 | 2 |
| #67745 | 2 |
| #67631 | 2 |
| #9307 | 3 |