Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #74154 | C2 | semidirect |
| 5. #70779 | C2 | semidirect |
| 6. #67737 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 15. #5093 | C4 | semidirect |
| 16. #5076 | C4 | semidirect |
| 135. C4×Dic3 | SD16 | semidirect |
| 358. C3 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83317 | 2 |
| #74154 | 2 |
| C3×#1517 | 2 |
| #71816 | 2 |
| #70779 | 2 |
| #67737 | 2 |
| #67631 | 2 |
| #9301 | 3 |