Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1166 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 6. #68997 | C2 | semidirect |
| 7. #68973 | C2 | semidirect |
| 248. C3 | #20730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5516 | 2 |
| #78620 | 2 |
| C3×#1822 | 2 |
| #71589 | 2 |
| #69990 | 2 |
| #68997 | 2 |
| #68973 | 2 |
| #20730 | 3 |