Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #79317 | C2 | semidirect |
| 5. #70777 | C2 | semidirect |
| 6. #67751 | C2 | semidirect |
| 7. #67742 | C2 | semidirect |
| 291. C3 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83282 | 2 |
| #79317 | 2 |
| C3×#1496 | 2 |
| #71803 | 2 |
| #70777 | 2 |
| #67751 | 2 |
| #67742 | 2 |
| #9008 | 3 |