Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #71425 | C2 | semidirect |
| 5. #71420 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67810 | C2 | semidirect |
| 279. C3 | #13129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2117 | 2 |
| #72008 | 2 |
| #72007 | 2 |
| #71425 | 2 |
| #71420 | 2 |
| #67813 | 2 |
| #67810 | 2 |
| #13129 | 3 |