Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
510 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 16. #4680 | C4 | semidirect |
| 122. C3×C8 | #103 | semidirect |
| 181. C8 | #810 | semidirect |
| 199. C3 | #9841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4680 | 2 |
| C3×#1845 | 2 |
| C2×#4455 | 2 |
| #69582 | 2 |
| #69579 | 2 |
| #9841 | 3 |