Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #78524 | C2 | semidirect |
| 3. #70784 | C2 | semidirect |
| 4. #70763 | C2 | semidirect |
| 5. #69860 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67716 | C2 | semidirect |
| 40. #1299 | D3 | semidirect |
| 408. C3 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79058 | 2 |
| #78524 | 2 |
| #70784 | 2 |
| #70763 | 2 |
| #69860 | 2 |
| C3×#1299 | 2 |
| #67716 | 2 |
| #9349 | 3 |