Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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. #79326 | C2 | semidirect |
| 3. C3×#1514 | C2 | semidirect |
| 4. #71801 | C2 | semidirect |
| 5. #69565 | C2 | semidirect |
| 6. #67757 | C2 | semidirect |
| 7. #67633 | C2 | semidirect |
| 15. #5086 | C4 | semidirect |
| 16. #5082 | C4 | semidirect |
| 17. #5074 | C4 | semidirect |
| 18. #5071 | C4 | semidirect |
| 39. #1514 | D3 | semidirect |
| 402. C3 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83309 | 2 |
| #79326 | 2 |
| C3×#1514 | 2 |
| #71801 | 2 |
| #69565 | 2 |
| #67757 | 2 |
| #67633 | 2 |
| #9370 | 3 |